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

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

Example 1 Find the area of the parallelogram

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.

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

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.

Example 2 Find the area of the trapezoid.

Example 3 Find the area of each trapezoid

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

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

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

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

Example 6 Find the area of each kite

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

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

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

Example 8 Find the area of the rhombus.

Example 9 Find the area of each rhombus

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

Example 11 Find the area of each figure