Answer
192 $units^{2}$
Work Step by Step
By using pythagoras theorem in right triangle ABD
$BD^{2}$ =$AB^{2}$ + $AD^{2}$
$20^{2}$ = $12^{2}$ + $AD^{2}$
$AD^{2}$ = $20^{2}$- $12^{2}$
= 400 - 144= 256
AD = $\sqrt 256$ = 16
We know in kites adjacent sides are equal
AB =BC =12
AD = CD = 16
The area of Kite ABCD = Area of $\triangle$ ABD + Area of $\triangle$ BCD
= $\frac{1}{2}$*AD*AB + $\frac{1}{2}$*DC*BC
= $\frac{1}{2}$*16*12 + $\frac{1}{2}$*16*12
= 96 + 96 = 192 $units^{2}$
