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

BD

C

Kite ABD DBCA A A

1 1

2 2BD AE BD EC

1

2BD AE EC

1

2BD AE

D BEE

Theorem The area of a kite equals half the product of its diagonals.

where d1 is the length of one diagonal, and d2 is the length of the other diagonal

1 2

1

2KiteA d d

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

d1

d2

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