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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now a smaller trapezoid: bases 3 cm and 5 cm, height 2 cm. First, what is 3 + 5? Yes, 8. Next, what is 8 × 2? Yes, 16. Now take half: ½ × 16 = 8, so the area is 8 square centimeters. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the area of a triangle with base 7 m and height 4 m?

   1. A11 square m
   2. B14 square m
   3. C14 m
   4. D28 square m

   How do you know?
3. 3

   Warm restartWhat is the area of a triangle with base 12 cm and height 5 cm?

   1. A17 square cm
   2. B30 square cm
   3. C30 cm
   4. D60 square cm

   How do you know?
4. 4

   Warm restartA triangle has an area of 36 square inches and a base of 9 inches. What is its height?

   1. A4 inches
   2. B8 inches
   3. C27 inches
   4. D324 inches

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the area of the trapezoidal driveway?

   1. A47 sq ft
   2. B120 sq ft
   3. C240 sq ft
   4. D480 sq ft

   Why is that the answer?
2. 6

   Think it throughHow many bags of concrete does the builder need?

   1. A6
   2. B24
   3. C40
   4. D240

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhy add the two parallel edges and then take half?

   1. ABecause trapezoids are half of rectangles
   2. BBecause the average of the two bases acts like one rectangle's width
   3. CBecause 20 + 12 = 32 is easier
   4. DBecause the height must be halved

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelIf 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?

Use the words

Fill each blank with a word from the bank.

• The space inside a trapezoid, found with A = ½(b₁ + b₂)h, is the ___.
• A quadrilateral with exactly one pair of parallel sides is a ___.
• Two sides that stay the same distance apart and never meet are ___.
• One of the two parallel sides of a trapezoid is ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Area of Trapezoids is forgetting the ½ in A = ½ × (b1 + b2) × h.
2. 10

   Say moreOn the grid you copied the trapezoid (bases 8 and 4, height 5), flipped it, and joined it to the original. What shape formed, and how does that explain the 1/2 in the formula?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The architecture firm's trapezoidal window has a top edge of 4 feet, a bottom edge of 8 feet, and a height of 5 feet.

   Show your work

Last check

These two come from Lesson 5.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A trapezoid has bases of 9 inches and 5 inches, and a height of 6 inches. What is its area?

   1. A27 sq in
   2. B42 sq in
   3. C42 in
   4. D84 sq in

   Explain your choice.
2. 13

   From Lesson 5.2Explain your thinking — A triangle has a base of 11 inches and a height of 8 inches. What is its area?

   1. A19 sq in
   2. B44 sq in
   3. C44 in
   4. D88 sq in

   How do you know?
3. 14

   From Lesson 5.2Why round up instead of down?

   1. ABecause 2 cans cover only 100 sq ft, which is not enough for 140
   2. BBecause paint is always sold in threes
   3. CBecause 2.8 rounds to 3 by the usual rule
   4. DBecause the wall might be bigger

   How do you know?

Be honest — this tells your teacher what to do next