Chapter 8.2, Problem 17E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercises 13 to 18, find the area of the given polygon.kite A B C D with B D = 12 m ∠ B A C = 45 ∘ ,   m ∠ B C A = 30 ∘

To determine

To Find:

Area of the kite.

Explanation

Formula Used:

The area A of a kite whose diagonals have lengths d1 and d2 is given by A=12d1d2.

Calculation:

It is given that the kite ABCD has one of the diagonals BD=d1=12 and mâˆ BAC=45Â°,mâˆ BCA=30Â°.

Letâ€™s draw another diagonal AC so that the diagonals BD and AC meet at a point be 'O'.

AC=AO+OCÂ â€¦ (1)

In kite, the diagonals d1 and d2 are perpendicular bisector of each other. That is âˆ BOA=âˆ BOC=90Â°.

As BD is the perpendicular bisector BO, BO=BD2=122=6

Now consider the triangle âˆ†AOB,

âˆ ABO=180-(âˆ BOA+âˆ BAO)

âˆ ABO=180-(90Â°+45Â°)

âˆ ABO=45Â°

Therefore, the triangle âˆ†AOB is a 45Â°:45Â°:90Â° right triangle

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