1. Areas of Trapezoids, Rhombuses, and Kites Objective: 1.To find the areas of trapezoids, rhombuses, and kites

2. Example 1 Find the area of the parallelogram

3. Bases and Heights basesaltitude height The parallel sides of a trapezoid are the bases. The altitude is a segment connecting the bases that is perpendicular to both. The length of the altitude (the distance between the bases) is the height.

4. Investigation 1 In this Investigation, you will discover a formula for computing the area of a trapezoid.

5. Area of a Trapezoid Theorem The area of a trapezoid is one half the product of the height and the sum of the lengths of the bases.

6. Example 2 Find the area of the trapezoid.

7. Example 3 Find the area of each trapezoid. 1. 2. 3.

8. Example 4 Find the value of x. 1. A = 12 yd 2 2. A = 39 cm 2

9. Investigation 2 The following investigation will demonstrate how to compute the area of a kite. Click on the picture to start.

10. Area of a Kite Theorem The area of a kite is one half the product of the lengths of its diagonals.

11. Example 5 Find the area of the kite to the nearest whole square unit.

12. Example 6 Find the area of each kite. 1. 2. 3.

13. Example 7 Find the value of x. 1. A = 60 m 2 2. A = 80 m 2 15 x

14. Investigation 3 This last investigation will demonstrate an alternate method of finding the area of a rhombus.

15. Area of a Rhombus Theorem The area of a rhombus is one half the product of the length of its diagonals.

16. Example 8 Find the area of the rhombus.

17. Example 9 Find the area of each rhombus. 1. 2. 3.

18. Example 10 Find the value of x. 1. A = 42 u 2 2. A = 300 m 2 x 12

19. Example 11 Find the area of each figure. 1. 2. 3.