Question

Given Kite ABCD whose diagonals intersect at E. If AD = AB = 5, AC = 9,

and AE = 3, find the area. *

Answer 1

36

Explanation:

AD = AB = 5,

AC = 9

AE = 3

Using Pythagoras :

ED^2 = AD^2 - AE^2

ED^2 = 5^2 - 3^2

ED^2 = 25 - 9

ED^2 = 16

ED = sqrt(16)

ED = 4

Therefore BE = 4

Therefore, length of diagonal BD = (4+4) = 8

Area of Kite = (Length of first diagonal × length of second diagonal) ÷ 2

Area = (9 × 8) ÷ 2

Area = 72 ÷ 2 = 36