Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3Determine the Area of Trapezoids

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
TrapezoidSpanish: Trapecio	A four-sided shape with just one pair of parallel sides.	top base and bottom base
ParallelSpanish: Paralelas	Two lines or sides that stay the same distance apart and never meet.	the two bases
Base 1 (b1)Spanish: Base 1 (b1)	One of the two parallel sides of a trapezoid.	If the bottom of the trapezoid is 10 ft, then b₁ = 10 ft in the formula A = ½(b₁ + b₂) × h
Base 2 (b2)Spanish: Base 2 (b2)	The other parallel side of a trapezoid.	If the top of the trapezoid is 6 ft, then b₂ = 6 ft; both bases are parallel to each other
HeightSpanish: Altura	The straight-up distance between the two parallel sides.	h, meets bases squarely
PerpendicularSpanish: Perpendicular	Two lines that meet to make a square corner (90 degrees).	The dashed height meets the base at a square corner — the small 90° box is what makes it perpendicular, not slanted.

How it worksWorked examplefinding a trapezoid's area by decomposing

These numbers are not on your problems. The steps are. Follow them with your own numbers.

An isosceles trapezoid has a top base of 8 m, a bottom base of 14 m, and a height of 6 m. Find the area.

Decompose it: a rectangle in the middle and two matching triangles on the ends.
Rectangle: top base by height. 8 × 6 = 48
Leftover bottom: 14 − 8 = 6, split evenly into two triangle bases of 3 m.
Each triangle ½ × 3 × 6 = 9, so two give 18. 48 + 18 = 66

Answer: The area of the trapezoid is 66 square meters (66 m²).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

An isosceles trapezoid has bases of 12 in. and 20 in. with a height of 7 in. Find the area.

Decompose into a rectangle and two matching triangles. Sketch the cuts.
Rectangle: × = in²
Leftover bottom: − = , so each triangle base is in.
Triangles: + = . Total: + = in²

Answer:area of the trapezoid

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

The two parallel bases are and .
I decomposed the trapezoid into and .
The pieces have areas , , and .
The total area is square units because .

Word bank trapezoidparallelbaseheightdecomposerectangletriangleleftoveraddtotalareasquare units

Watch outA common mistake

A common mistake in Area of Trapezoids is forgetting the ½ in A = ½ × (b1 + b2) × h. After adding the bases and multiplying by the height, students stop there instead of taking half — for example, with bases 6 ft and 10 ft and a height of 4 ft, they compute (6 + 10) × 4 = 64 sq ft instead of taking half to get the correct 32 sq ft. That unhalved number is really the area of the parallelogram made from two trapezoids, not the area of one trapezoid. Before you submit, always ask: "Did I take half of my last answer?"

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3Determine the Area of Trapezoids

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Use the formula A = ½ × (b₁ + b₂) × h to find the area of each trapezoid.

Trapezoid Base 1 Base 2 Height Area
Shape A 4 ft 6 ft 3 ft
Shape B 8 ft 12 ft 5 ft

Hint Each row lists Base 1, Base 2, and Height — the Area column is the only blank to fill.
Show your work

Trapezoid	Base 1	Base 2	Height	Area
Shape A	4 ft	6 ft	3 ft
Shape B	8 ft	12 ft	5 ft

Part 2Apply itreal-world problems

2Circle the letter of the best answer. Show how you know.
What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?
1. A24 sq cm
2. B32 sq cm
3. C40 sq cm
4. D64 sq cm
Hint A trapezoid has two bases (6 cm and 10 cm) plus a height (4 cm) — all three belong in the formula.
Formula

Put the numbers in

Work it out

Answer with its unit
1. 1Name itWhich measure is asked?
2. 2Write the formulaBefore any numbers.
3. 3SubstituteMatch each letter.
4. 4Unitunits, sq units, or cubic?
3Circle the letter of the best answer. Show how you know.
A trapezoid has an area of 45 sq ft, bases of 7 ft and 11 ft. What is the height?
1. A3 ft
2. B5 ft
3. C9 ft
4. D10 ft
Hint You already know the area (45 sq ft) and both bases (7 ft and 11 ft) — the height is what's missing.
Formula

Put the numbers in

Work it out

Answer with its unit
1. 1Name itWhich measure is asked?
2. 2Write the formulaBefore any numbers.
3. 3SubstituteMatch each letter.
4. 4Unitunits, sq units, or cubic?
4Circle the letter of the best answer. Show how you know.
What is the first step when finding the area of a trapezoid?
1. AMultiply the two bases
2. BSubtract the shorter base from the longer base
3. CAdd the two bases together
4. DDivide the height by 2
Hint Look at the trapezoid formula A = ½ × (b₁ + b₂) × h. Parentheses show what happens first.
Show your work
5Circle the letter of the best answer. Show how you know.
A trapezoid has bases of 5 in and 9 in, and a height of 6 in. What is its area?
1. A27 sq in
2. B30 sq in
3. C42 sq in
4. D84 sq in
Hint Circle the two bases (5 in and 9 in) and the height (6 in) — the trapezoid formula uses all three.
Formula

Put the numbers in

Work it out

Answer with its unit
1. 1Name itWhich measure is asked?
2. 2Write the formulaBefore any numbers.
3. 3SubstituteMatch each letter.
4. 4Unitunits, sq units, or cubic?

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Find the Missing Half
1. 1Read the blueprintA trapezoid-shaped patio stone has b1 = 4 ft, b2 = 8 ft, and h = 6 ft.
2. 2Write the formulaA = ½ × (b1 + b2) × h
3. 3Add the bases, then multiply by height(4 + 8) × 6 = 12 × 6 = 72
4. 4State the areaA = 72 sq ft
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Compare the last step to the formula A = ½ × (b1 + b2) × h — what operation is missing?
Correct work
Correct answer:

Explain your thinkingIf you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?

Sentence starter The area of the trapezoid is 1/2 x (___ + ___) x ___ = 1/2 x ___ x ___ = ___ square feet.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3Determine the Area of Trapezoids

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Complete the table.

Trapezoid Base 1 Base 2 Height Area
Window A 8 ft 4 ft 5 ft
Window B 12 ft 6 ft 4 ft
Window C 10 ft 8 ft 72 sq ft
Window D 5 ft 6 ft 48 sq ft

Show your work
2Write the letter of the matching item on each line.
Match each shape to its area.
1. Trapezoid b₁=10, b₂=6, h=4
2. Trapezoid b₁=8, b₂=4, h=5
3. Trapezoid b₁=12, b₂=8, h=4
4. Triangle b=14, h=6
5. Parallelogram b=9, h=5
6. Rectangle 7×3
- A32 sq units
- B30 sq units
- C40 sq units
- D42 sq units
- E45 sq units
- F21 sq units
3Write the name of the correct group on each line.
Calculate the area of each trapezoid, then sort by whether the area is greater than 40 sq units or not.

Groups: Area > 40 sq units Area ≤ 40 sq units
- b₁=10, b₂=6, h=4
- b₁=12, b₂=8, h=5
- b₁=6, b₂=4, h=7
- b₁=9, b₂=7, h=6
- b₁=5, b₂=3, h=8
- b₁=14, b₂=6, h=5
4Mark and label each value on the number line.

Find the missing height: b₁=6, b₂=10, A=48
Show your thinking

Trapezoid	Base 1	Base 2	Height	Area
Window A	8 ft	4 ft	5 ft
Window B	12 ft	6 ft	4 ft
Window C	10 ft		8 ft	72 sq ft
Window D		5 ft	6 ft	48 sq ft

Part 2Explain and correctreasoning

5Find the mistake. Explain it, then show the correct work.
Using the Wrong Height
1. 1Read the blueprintA trapezoid window has b1 = 7 ft and b2 = 13 ft. The slanted side measures 10 ft, and the straight-up height between the bases is 6 ft.
2. 2Write the formulaA = ½ × (b1 + b2) × h
3. 3Substitute valuesA = ½ × (7 + 13) × 10
4. 4CalculateA = ½ × 20 × 10 = 100 sq ft
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingIf you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.3Determine the Area of Trapezoids

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.

Part 1Understand the ideamodels and meaning

1Plot and label each point on the grid.

Plot the trapezoid and calculate its area.
Show your thinking

Part 2Explain and correctreasoning

2Find the mistake. Explain it, then show the correct work.
Find the Area Error
1. 1Identify the bases and heightb₁ = 10 m, b₂ = 6 m, h = 7 m
2. 2Write the formulaA = ½ × (b₁ + b₂) × h
3. 3Substitute valuesA = ½ × (10 + 6) × 7
4. 4CalculateA = (10 + 6) × 7 = 112 sq m
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
3Answer in complete sentences.

A trapezoid and a parallelogram both have a height of 8 ft. The trapezoid has bases of 5 ft and 11 ft. The parallelogram has a base of 7 ft. Which shape has the greater area? Explain your reasoning using the formulas.
Write your answer

Explain your thinkingIf you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help