← One number -- the base's sides -- fixes every count a prism has · Net and Solid Structure

One number -- the base's sides -- fixes every count a prism has · 12 practice problems

6.G.A.46.EE.B.7

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 15

A prism has 55 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 5 faces. We want its edges and its vertices added together.

Givens
  • The prism has 5 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 5 = n + 2.
n=5−2=3n = 5 - 2 = 3
It is a triangular prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 3 edges on each base and 3 uprights joining them, and each base contributes 3 corners.
edges=3n=9,vertices=2n=6\text{edges} = 3n = 9,\quad \text{vertices} = 2n = 6
9 edges and 6 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
9+6=159 + 6 = 15
15 in all.
Answer: 15
4 · Reviewdoes it hold up?

Euler's rule holds: 5 faces minus 9 edges plus 6 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a triangular prism and counting works too, and agrees -- but the drawing gets unreliable well before 3 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 2 easy answer: 20

A prism has 66 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 6 faces. We want its edges and its vertices added together.

Givens
  • The prism has 6 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 6 = n + 2.
n=6−2=4n = 6 - 2 = 4
It is a square prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 4 edges on each base and 4 uprights joining them, and each base contributes 4 corners.
edges=3n=12,vertices=2n=8\text{edges} = 3n = 12,\quad \text{vertices} = 2n = 8
12 edges and 8 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
12+8=2012 + 8 = 20
20 in all.
Answer: 20
4 · Reviewdoes it hold up?

Euler's rule holds: 6 faces minus 12 edges plus 8 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a square prism and counting works too, and agrees -- but the drawing gets unreliable well before 4 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 3 easy answer: 25

A prism has 77 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 7 faces. We want its edges and its vertices added together.

Givens
  • The prism has 7 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 7 = n + 2.
n=7−2=5n = 7 - 2 = 5
It is a pentagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 5 edges on each base and 5 uprights joining them, and each base contributes 5 corners.
edges=3n=15,vertices=2n=10\text{edges} = 3n = 15,\quad \text{vertices} = 2n = 10
15 edges and 10 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
15+10=2515 + 10 = 25
25 in all.
Answer: 25
4 · Reviewdoes it hold up?

Euler's rule holds: 7 faces minus 15 edges plus 10 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a pentagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 5 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 4 easy answer: 30

A prism has 88 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 8 faces. We want its edges and its vertices added together.

Givens
  • The prism has 8 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 8 = n + 2.
n=8−2=6n = 8 - 2 = 6
It is a hexagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 6 edges on each base and 6 uprights joining them, and each base contributes 6 corners.
edges=3n=18,vertices=2n=12\text{edges} = 3n = 18,\quad \text{vertices} = 2n = 12
18 edges and 12 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
18+12=3018 + 12 = 30
30 in all.
Answer: 30
4 · Reviewdoes it hold up?

Euler's rule holds: 8 faces minus 18 edges plus 12 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a hexagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 6 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 5 medium answer: 35

A prism has 99 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 9 faces. We want its edges and its vertices added together.

Givens
  • The prism has 9 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 9 = n + 2.
n=9−2=7n = 9 - 2 = 7
It is a heptagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 7 edges on each base and 7 uprights joining them, and each base contributes 7 corners.
edges=3n=21,vertices=2n=14\text{edges} = 3n = 21,\quad \text{vertices} = 2n = 14
21 edges and 14 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
21+14=3521 + 14 = 35
35 in all.
Answer: 35
4 · Reviewdoes it hold up?

Euler's rule holds: 9 faces minus 21 edges plus 14 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a heptagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 7 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 6 medium answer: 40

A prism has 1010 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 10 faces. We want its edges and its vertices added together.

Givens
  • The prism has 10 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 10 = n + 2.
n=10−2=8n = 10 - 2 = 8
It is a octagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 8 edges on each base and 8 uprights joining them, and each base contributes 8 corners.
edges=3n=24,vertices=2n=16\text{edges} = 3n = 24,\quad \text{vertices} = 2n = 16
24 edges and 16 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
24+16=4024 + 16 = 40
40 in all.
Answer: 40
4 · Reviewdoes it hold up?

Euler's rule holds: 10 faces minus 24 edges plus 16 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a octagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 8 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 7 medium answer: 45

A prism has 1111 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 11 faces. We want its edges and its vertices added together.

Givens
  • The prism has 11 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 11 = n + 2.
n=11−2=9n = 11 - 2 = 9
It is a nonagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 9 edges on each base and 9 uprights joining them, and each base contributes 9 corners.
edges=3n=27,vertices=2n=18\text{edges} = 3n = 27,\quad \text{vertices} = 2n = 18
27 edges and 18 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
27+18=4527 + 18 = 45
45 in all.
Answer: 45
4 · Reviewdoes it hold up?

Euler's rule holds: 11 faces minus 27 edges plus 18 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a nonagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 9 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 8 medium answer: 50

A prism has 1212 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 12 faces. We want its edges and its vertices added together.

Givens
  • The prism has 12 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 12 = n + 2.
n=12−2=10n = 12 - 2 = 10
It is a decagonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 10 edges on each base and 10 uprights joining them, and each base contributes 10 corners.
edges=3n=30,vertices=2n=20\text{edges} = 3n = 30,\quad \text{vertices} = 2n = 20
30 edges and 20 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
30+20=5030 + 20 = 50
50 in all.
Answer: 50
4 · Reviewdoes it hold up?

Euler's rule holds: 12 faces minus 30 edges plus 20 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a decagonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 10 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 9 hard answer: 60

A prism has 1414 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 14 faces. We want its edges and its vertices added together.

Givens
  • The prism has 14 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 14 = n + 2.
n=14−2=12n = 14 - 2 = 12
It is a 12-gonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 12 edges on each base and 12 uprights joining them, and each base contributes 12 corners.
edges=3n=36,vertices=2n=24\text{edges} = 3n = 36,\quad \text{vertices} = 2n = 24
36 edges and 24 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
36+24=6036 + 24 = 60
60 in all.
Answer: 60
4 · Reviewdoes it hold up?

Euler's rule holds: 14 faces minus 36 edges plus 24 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a 12-gonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 12 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 10 hard answer: 70

A prism has 1616 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 16 faces. We want its edges and its vertices added together.

Givens
  • The prism has 16 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 16 = n + 2.
n=16−2=14n = 16 - 2 = 14
It is a 14-gonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 14 edges on each base and 14 uprights joining them, and each base contributes 14 corners.
edges=3n=42,vertices=2n=28\text{edges} = 3n = 42,\quad \text{vertices} = 2n = 28
42 edges and 28 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
42+28=7042 + 28 = 70
70 in all.
Answer: 70
4 · Reviewdoes it hold up?

Euler's rule holds: 16 faces minus 42 edges plus 28 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a 14-gonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 14 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 11 hard answer: 90

A prism has 2020 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 20 faces. We want its edges and its vertices added together.

Givens
  • The prism has 20 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 20 = n + 2.
n=20−2=18n = 20 - 2 = 18
It is a 18-gonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 18 edges on each base and 18 uprights joining them, and each base contributes 18 corners.
edges=3n=54,vertices=2n=36\text{edges} = 3n = 54,\quad \text{vertices} = 2n = 36
54 edges and 36 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
54+36=9054 + 36 = 90
90 in all.
Answer: 90
4 · Reviewdoes it hold up?

Euler's rule holds: 20 faces minus 54 edges plus 36 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a 18-gonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 18 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.
Variant 12 hard answer: 125

A prism has 2727 faces. How many edges and vertices does it have in all?

Show solution
1 · Understandwhat's really being asked

A prism has 27 faces. We want its edges and its vertices added together.

Givens
  • The prism has 27 faces.
Unknowns
  • The number of edges plus the number of vertices.
Constraints
  • It is a prism, so it has two congruent bases joined by rectangles.
2 · Planchoose the strategy

#13 Convert to Algebra · also uses: #17 Visualize Spatial Relationships#5 Look for a Pattern

Do not try to picture the solid first. Every count a prism has is a formula in the number of sides on its base, so get that number from the faces and the rest follows by substitution.

3 · Execute4 carry out the plan

1Write the faces in terms of the base

#13 Convert to Algebra 6.G.A.4
A prism has one side face per base edge, plus the two bases.
faces=n+2\text{faces} = n + 2
The base's sides decide everything.

2Find the base

#13 Convert to Algebra 6.EE.B.7
Solve 27 = n + 2.
n=27−2=25n = 27 - 2 = 25
It is a 25-gonal prism.

3Count edges and vertices

#17 Visualize Spatial Relationships 6.G.A.4
There are 25 edges on each base and 25 uprights joining them, and each base contributes 25 corners.
edges=3n=75,vertices=2n=50\text{edges} = 3n = 75,\quad \text{vertices} = 2n = 50
75 edges and 50 vertices.

4Add the two

#5 Look for a Pattern 6.EE.B.7
The question asks for both together.
75+50=12575 + 50 = 125
125 in all.
Answer: 125
4 · Reviewdoes it hold up?

Euler's rule holds: 27 faces minus 75 edges plus 50 vertices is 2, which is 2 for every solid of this kind.

Another way: Drawing a 25-gonal prism and counting works too, and agrees -- but the drawing gets unreliable well before 25 sides.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Relating a prism's faces, edges and vertices to its base.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the number of base sides, then substituting it.
💡Takeaway. Find the one number a shape is built from, and every other count is a formula away.