1. 1 In this chapter, you have developed several different strategies for finding the areas of shapes. You have found the sums of the areas of multiple smaller parts. You have rearranged smaller parts into rectangles to find areas. You have also made shapes bigger to find their areas. You have developed quite a repertoire of strategies! In this lesson, you will focus on how to choose a strategy to find the area of a new shape: a trapezoid. As you work with your team, practice visualizing how each shape can be changed or rearranged. Ask each other these questions as you work: What strategy should we choose? Which lengths are important?

2. 2 a)How can we cut and rearrange a trapezoid into another shape for which we can find the area? b)What shapes can we make from two identical trapezoids? c)Which lengths are needed to find the area? d)How is the area of each original trapezoid related to the area of the other shapes you created? 96. AREA CHALLENGE — TRAPEZOIDS Trapezoids are shapes like the ones at right. A trapezoid has four sides and at least one pair of opposite sides that are parallel. Will finding the area of an unfamiliar shape by cutting and rearranging pieces to form a parallelogram or rectangle work to find the area of a trapezoid? To investigate how to find the area of this new shape, get a set of three trapezoids from the Lesson 5.3.4A Resource Page for your team. Your team may want to explore using Shape 3 and Shape 5 in the Area Decomposer: Fig.3 Fig.5 (Desmos) or explore using the Trapezoid Decomposer (Desmos).Lesson 5.3.4A Resource PageShape 3Shape 5Trapezoid Decomposer Your Task: Work with your team to identify at least two ways to rearrange a trapezoid into another shape (or set of shapes) for which you could find the area. Then discuss how you could find the area of each original trapezoid. Use the Discussion Points below to getstarted.

3. 3 97. Sheila thought she could make a trapezoid into a parallelogram, and then into a rectangle. She started by folding her trapezoid so that the two parallel sides lined up. Then she cut along the fold line (the dashed line in the picture). a)Fold and cut one of your trapezoids the same way Sheila did. What two new shapes have you created? b)How can Sheila rearrange her two pieces to make one parallelogram? Sketch her shape. c)Locate the base and the height of the parallelogram. Where could she find these lengths on her original trapezoid?

4. 4 98. AREA OF A TRAPEZOID Dejon’s homework tonight includes a problem where he has to find the area of the trapezoid at right. a)Draw a copy of Dejon’s trapezoid on your paper. Then choose a way to form a parallelogram. Sketch the rearrangement on your paper and label the base and height of the parallelogram. b)Find the lengths on the trapezoid that make the base of the parallelogram. These lengths are called the bases of the trapezoid. c)Where can you see the height of the parallelogram on the trapezoid? What does it measure? d)Find the area of the new parallelogram or rectangle. How is this area related to the area of the trapezoid? Explain how you found your answer. e)If you have not already done so, find the area of the trapezoid.

5. 5 99. PARK PROBLEM The city council is trying to decide how much to budget for mowing the grass in the city park shown in the diagram at right. The park is all grass except for a playground area, a picnic area, and basketball courts. Using what your team knows about finding the areas of rectangles, parallelograms, triangles, and trapezoids, and using the Lesson 5.3.4C Resource Page, calculate the area of the park that will need to be mowed. Assume that all angles appearing to be right angles are actually right angles. If possible, find two different ways to find the total area. Be sure to show all of your work so that you can explain your strategies to other teams. Lesson 5.3.4C Resource Page

6. 6 100. LEARNING LOG Title this entry “Area of a Trapezoid” and include today’s date In your Learning Log, describe how to find the area of a trapezoid. This entry does not ask you simply to write a formula. Be sure to… a)Sketch an example shape and show how you can find the area. b)Explain how finding the area of a trapezoid is similar to finding the areas of other types of shapes. Also, explain how it is different..

7. 7 Tonight’s homework is… 5.3.4 Review & Preview, problems # 101-105 Show all work and justify your answers for full credit. Review “Methods and Meanings” Area of a Triangle.