11.4 The Area Of a Kite Objective: After studying this section you will be able to find the areas of kites.

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11.4 The Area Of a Kite Objective: After studying this section you will be able to find the areas of kites

Remember When We Learned Properties of Special Quadrilaterals? 1. In a kite, the diagonals are perpendicular. 2. The longer diagonal bisects the shorter diagonal. This means the kite can be divided into 2 isosceles triangles with a common base…so its area will equal the sum of the areas of the two triangles.

Let’s A B D C D B E E

TheoremThe area of a kite equals half the product of its diagonals. where d 1 is the length of one diagonal, and d 2 is the length of the other diagonal But Wait! Did you notice BD and AC are the diagonals of the kite?! (We just proved the formula for area of a kite…no big deal!)

Just a Note… This formula can be applied to any kite, including the special cases of a rhombus and a square d1d1 d2d2

Example #1 Find the area of a kite with diagonals 9 and 14

Example #2 Find the area of a rhombus whose perimeter is 20 and whose longer diagonal is 8.

Homework Worksheet 11.4