Lesson 5.35.3 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h — one step at a time, with support.
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
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?"
Lesson 5.35.3 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h — one step at a time, with support.
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1Complete each step, then write the final answer.
The two bases are parallel. The height connects them. A trapezoid has bases of 6 cm and 9 cm. Its height is 4 cm. Find its area.
- 1Add the two bases. What do you get?
- 2Multiply the sum by the height.
- 3Take half. What is the area?
Final answer: -
2Complete each step, then write the final answer.
The slanted sides are not bases and not the height. A trapezoid has bases of 5 m and 11 m and a height of 4 m. Each slanted side is 5 m. Find its area.
- 1Which sides are the bases? Which length is the height?
- 2Add the bases. Multiply by the height.
- 3Take half. What is the area?
Final answer: -
3Complete each step, then write the final answer.
A trapezoid has bases of 2 in and 4 in. Its height is 3 in. Find its area.
Show your workHint Add the bases. Multiply by the height. Then take half.
Final answer: -
4Complete each step, then write the final answer.
A trapezoid has bases of 12 ft and 8 ft. Its height is 7 ft. Find its area.
Show your workHint Add the bases first. Then multiply by 7 and take half.
Final answer: -
5Complete each step, then write the final answer.
A garden bed is a trapezoid. Its parallel sides are 10 m and 14 m long. They are 5 m apart. What is the area of the garden bed?
Show your workHint The parallel sides are the bases. The distance between them is the height.
Final answer: -
6Complete each step, then write the final answer.
Rosa finds the area of a trapezoid with bases 7 cm and 3 cm and height 6 cm. She writes 7 × 6 = 42. What is the correct area?
Show your workHint Rosa used only one base. A trapezoid has two bases.
Final answer:
Explain your thinkingWhy do we add both bases before we multiply? Use Rosa’s mistake to explain.
Sentence starter A trapezoid has ___ bases, so we ___. · Rosa got 42 because she ___.