The right-angle mark makes the height a known number
6.G.A.16.NS.B.3
Generated variants — 12
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 12.8 cm and 15 cm and is 8 cm tall. Triangle DEC is one 2th of it, and we want EC.
Givens
- AD is 12.8 cm and BC is 15 cm.
- The trapezoid is 8 cm tall.
- Triangle DEC has one 2th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 2th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 13.9 cm out of BC's 15 cm, so the triangle really does sit inside the trapezoid, and its area 55.6 is one 2th of 111.2.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 6.4 cm and 14.4 cm and is 17 cm tall. Triangle DEC is one 8th of it, and we want EC.
Givens
- AD is 6.4 cm and BC is 14.4 cm.
- The trapezoid is 17 cm tall.
- Triangle DEC has one 8th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 8th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 2.6 cm out of BC's 14.4 cm, so the triangle really does sit inside the trapezoid, and its area 22.1 is one 8th of 176.8.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 8.4 cm and 13 cm and is 17 cm tall. Triangle DEC is one 5th of it, and we want EC.
Givens
- AD is 8.4 cm and BC is 13 cm.
- The trapezoid is 17 cm tall.
- Triangle DEC has one 5th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 5th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 4.28 cm out of BC's 13 cm, so the triangle really does sit inside the trapezoid, and its area 36.38 is one 5th of 181.9.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 12.4 cm and 18 cm and is 8 cm tall. Triangle DEC is one 4th of it, and we want EC.
Givens
- AD is 12.4 cm and BC is 18 cm.
- The trapezoid is 8 cm tall.
- Triangle DEC has one 4th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 4th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 7.6 cm out of BC's 18 cm, so the triangle really does sit inside the trapezoid, and its area 30.4 is one 4th of 121.6.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 11.8 cm and 18.6 cm and is 9 cm tall. Triangle DEC is one 5th of it, and we want EC.
Givens
- AD is 11.8 cm and BC is 18.6 cm.
- The trapezoid is 9 cm tall.
- Triangle DEC has one 5th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 5th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 6.08 cm out of BC's 18.6 cm, so the triangle really does sit inside the trapezoid, and its area 27.36 is one 5th of 136.8.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 13.8 cm and 16.8 cm and is 20 cm tall. Triangle DEC is one 2th of it, and we want EC.
Givens
- AD is 13.8 cm and BC is 16.8 cm.
- The trapezoid is 20 cm tall.
- Triangle DEC has one 2th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 2th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 15.3 cm out of BC's 16.8 cm, so the triangle really does sit inside the trapezoid, and its area 153 is one 2th of 306.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 13.6 cm and 17 cm and is 20 cm tall. Triangle DEC is one 15th of it, and we want EC.
Givens
- AD is 13.6 cm and BC is 17 cm.
- The trapezoid is 20 cm tall.
- Triangle DEC has one 15th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 15th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 2.04 cm out of BC's 17 cm, so the triangle really does sit inside the trapezoid, and its area 20.4 is one 15th of 306.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 16.2 cm and 21 cm and is 6 cm tall. Triangle DEC is one 20th of it, and we want EC.
Givens
- AD is 16.2 cm and BC is 21 cm.
- The trapezoid is 6 cm tall.
- Triangle DEC has one 20th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 20th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 1.86 cm out of BC's 21 cm, so the triangle really does sit inside the trapezoid, and its area 5.58 is one 20th of 111.6.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 16 cm and 21.6 cm and is 14 cm tall. Triangle DEC is one 5th of it, and we want EC.
Givens
- AD is 16 cm and BC is 21.6 cm.
- The trapezoid is 14 cm tall.
- Triangle DEC has one 5th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 5th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 7.52 cm out of BC's 21.6 cm, so the triangle really does sit inside the trapezoid, and its area 52.64 is one 5th of 263.2.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 15.4 cm and 20.2 cm and is 22 cm tall. Triangle DEC is one 5th of it, and we want EC.
Givens
- AD is 15.4 cm and BC is 20.2 cm.
- The trapezoid is 22 cm tall.
- Triangle DEC has one 5th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 5th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 7.12 cm out of BC's 20.2 cm, so the triangle really does sit inside the trapezoid, and its area 78.32 is one 5th of 391.6.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 14 cm and 22.6 cm and is 16 cm tall. Triangle DEC is one 2th of it, and we want EC.
Givens
- AD is 14 cm and BC is 22.6 cm.
- The trapezoid is 16 cm tall.
- Triangle DEC has one 2th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 2th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 18.3 cm out of BC's 22.6 cm, so the triangle really does sit inside the trapezoid, and its area 146.4 is one 2th of 292.8.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.
In the figure at the right, triangle DEC has the area of trapezoid ABCD. How long is segment EC, in ?
Show solution
1 · Understandwhat's really being asked
A trapezoid has parallel sides 8.2 cm and 11.8 cm and is 23 cm tall. Triangle DEC is one 5th of it, and we want EC.
Givens
- AD is 8.2 cm and BC is 11.8 cm.
- The trapezoid is 23 cm tall.
- Triangle DEC has one 5th of the trapezoid's area.
- DE meets BC at a right angle.
Unknowns
- The length of EC.
Constraints
- E lies on BC, so EC is part of the bottom side.
2 · Planchoose the strategy
#7 Identify Subproblems
The right angle at E is the key: it makes DE the trapezoid's own height, so the triangle's area formula has just one unknown left. Find the trapezoid's area, take a share of it, then undo the formula.
3 · Execute4 carry out the plan
1Find the trapezoid's area
2Take one 5th of it
3Read the triangle's height off the right angle
4Undo the triangle's area formula
4 · Reviewdoes it hold up?
EC is 4 cm out of BC's 11.8 cm, so the triangle really does sit inside the trapezoid, and its area 46 is one 5th of 230.
Standardsmin grade 6
6.G.A.1Find area of triangles, quadrilaterals, polygons by composing/decomposing — Using the trapezoid and triangle area formulas.6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals to get the share and then the length.