Practice · A prism has two bases and one upright per base edge · Sensim Math

Variant 1 easy answer: 72 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 5, 9 and 7 cm and whose height is 10 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 5 cm, 9 cm and 7 cm.
The three side rectangles are 10 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

5 + 9 + 7 = 21

One triangle is 21 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

21 \times 2 = 42

The two triangles give 42 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 10 cm.

10 \times 3 = 30

The uprights give 30 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

42 + 30 = 72

The edges total 72 cm.

Answer: 72 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 2 easy answer: 79 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 6, 9 and 8 cm and whose height is 11 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 6 cm, 9 cm and 8 cm.
The three side rectangles are 11 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

6 + 9 + 8 = 23

One triangle is 23 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

23 \times 2 = 46

The two triangles give 46 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 11 cm.

11 \times 3 = 33

The uprights give 33 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

46 + 33 = 79

The edges total 79 cm.

Answer: 79 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 3 easy answer: 88 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 9, 12 and 11 cm and whose height is 8 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 9 cm, 12 cm and 11 cm.
The three side rectangles are 8 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

9 + 12 + 11 = 32

One triangle is 32 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

32 \times 2 = 64

The two triangles give 64 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 8 cm.

8 \times 3 = 24

The uprights give 24 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

64 + 24 = 88

The edges total 88 cm.

Answer: 88 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 4 easy answer: 86 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 7, 12 and 9 cm and whose height is 10 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 7 cm, 12 cm and 9 cm.
The three side rectangles are 10 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

7 + 12 + 9 = 28

One triangle is 28 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

28 \times 2 = 56

The two triangles give 56 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 10 cm.

10 \times 3 = 30

The uprights give 30 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

56 + 30 = 86

The edges total 86 cm.

Answer: 86 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 5 medium answer: 89 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 6, 11 and 8 cm and whose height is 13 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 6 cm, 11 cm and 8 cm.
The three side rectangles are 13 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

6 + 11 + 8 = 25

One triangle is 25 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

25 \times 2 = 50

The two triangles give 50 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 13 cm.

13 \times 3 = 39

The uprights give 39 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

50 + 39 = 89

The edges total 89 cm.

Answer: 89 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 6 medium answer: 96 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 8, 13 and 9 cm and whose height is 12 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 8 cm, 13 cm and 9 cm.
The three side rectangles are 12 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

8 + 13 + 9 = 30

One triangle is 30 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

30 \times 2 = 60

The two triangles give 60 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 12 cm.

12 \times 3 = 36

The uprights give 36 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

60 + 36 = 96

The edges total 96 cm.

Answer: 96 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 7 medium answer: 88 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 11, 14 and 10 cm and whose height is 6 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 11 cm, 14 cm and 10 cm.
The three side rectangles are 6 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

11 + 14 + 10 = 35

One triangle is 35 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

35 \times 2 = 70

The two triangles give 70 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 6 cm.

6 \times 3 = 18

The uprights give 18 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

70 + 18 = 88

The edges total 88 cm.

Answer: 88 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 8 medium answer: 74 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 4, 7 and 5 cm and whose height is 14 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 4 cm, 7 cm and 5 cm.
The three side rectangles are 14 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

4 + 7 + 5 = 16

One triangle is 16 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

16 \times 2 = 32

The two triangles give 32 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 14 cm.

14 \times 3 = 42

The uprights give 42 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

32 + 42 = 74

The edges total 74 cm.

Answer: 74 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 9 hard answer: 91 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 7, 10 and 6 cm and whose height is 15 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 7 cm, 10 cm and 6 cm.
The three side rectangles are 15 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

7 + 10 + 6 = 23

One triangle is 23 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

23 \times 2 = 46

The two triangles give 46 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 15 cm.

15 \times 3 = 45

The uprights give 45 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

46 + 45 = 91

The edges total 91 cm.

Answer: 91 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 10 hard answer: 101 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 10, 15 and 12 cm and whose height is 9 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 10 cm, 15 cm and 12 cm.
The three side rectangles are 9 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

10 + 15 + 12 = 37

One triangle is 37 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

37 \times 2 = 74

The two triangles give 74 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 9 cm.

9 \times 3 = 27

The uprights give 27 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

74 + 27 = 101

The edges total 101 cm.

Answer: 101 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 11 hard answer: 86 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 5, 8 and 6 cm and whose height is 16 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 5 cm, 8 cm and 6 cm.
The three side rectangles are 16 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

5 + 8 + 6 = 19

One triangle is 19 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

19 \times 2 = 38

The two triangles give 38 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 16 cm.

16 \times 3 = 48

The uprights give 48 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

38 + 48 = 86

The edges total 86 cm.

Answer: 86 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

Variant 12 hard answer: 105 cm

The net at the right is folded to make a pencil case. What is the sum of all the edge lengths of the case, in $\text{cm}$ ?

Show solution

1 · Understandwhat's really being asked

A net folds into a triangular prism whose base sides are 12, 17 and 13 cm and whose height is 7 cm. We want every edge of the finished case added up.

Givens

The triangular base has sides 12 cm, 17 cm and 13 cm.
The three side rectangles are 7 cm tall.
The two triangles on the net are congruent.

Unknowns

The sum of all the prism's edge lengths.

Constraints

The net folds up with no overlap, so every edge of the solid comes from the net.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #10 Create a Physical Representation#2 Make a Systematic List

Sort the prism's edges by kind before counting: a triangular prism has two base triangles and one upright per base edge. Counting off the flat net instead risks missing the second triangle, which is only drawn once.

3 · Execute4 carry out the plan

1Find the base's perimeter

#2 Make a Systematic List 6.G.A.4

Add the triangle's three sides.

12 + 17 + 13 = 42

One triangle is 42 cm around.

2There are two of them

#17 Visualize Spatial Relationships 6.G.A.4

A prism is closed by a base at each end, and they are congruent.

42 \times 2 = 84

The two triangles give 84 cm.

3Count the uprights

#10 Create a Physical Representation 6.G.A.4

One upright joins each pair of matching base corners, so there are 3 of them, each 7 cm.

7 \times 3 = 21

The uprights give 21 cm.

4Add the two kinds

#2 Make a Systematic List 6.G.A.4

Every edge of the prism is either a base edge or an upright.

84 + 21 = 105

The edges total 105 cm.

Answer: 105 cm

4 · Reviewdoes it hold up?

A triangular prism has 9 edges: 3 + 3 base edges and 3 uprights. Counting them here gives 3 + 3 + 3, so nothing is missing.

Another way: Tracing the net edge by edge also works, but each of the two creases between rectangles is one upright shared by two faces, so it must not be counted twice.

Standardsmin grade 6

6.G.A.4 Surface area using nets of 3D figures — Reading the solid's edges off its net without double counting.

💡Takeaway. A net draws each face once, but a prism has two bases. Count the solid's edges by kind, not by what you can see on the paper.

A prism has two bases and one upright per base edge · 12 practice problems

Generated variants — 12

Givens

Unknowns

Constraints

Givens

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Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

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Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints