Question

Find the area of the kite QRST. HELP PLEASE!!!

A. 90m^2
B. 108m^2
C. 216 m^2
D. 135 m^2

Answer 1

`A_(T)=135 m^{2`

Explanation:

Hello

To solve this problem we can divide the kite into simpler geometric figures to find its area, we have four triangles

the area of a triangle =(b*h)/2

b is the base and his the heigth

Step 1

triangle 1 (LEFT UP)

`b=9\ m\\\ h= 9\ m\\A=(9 m* 9m)/(2)\\\\A_(1) =40.5\ m^(2)`

Step 2

triangle 2 (RIGHT UP)

`b=9\ m\\\ h= 9\ m\\A=(9 m* 9m)/(2)\\\\A_(2) =40.5\ m^(2)`

Step 3

triangle 3 (LEFT DOWN)

`b=9\ m\\\ h= 6\ m\\A=(9 m* 6m)/(2)\\\\A_(3) =27\ m^(2)`

Step 4

triangle 4 (RIGHT DOWN)

`b=9\ m\\\ h= 6\ m\\A=(9 m* 6m)/(2)\\\\A_(4) =27\ m^(2)`

Step 5

Total Area

the total area is

`A_(T)=A_(1)+A_(2)+A_(3)+A_(4)   \\A_(T)=(40.5+40.5+27+27)m^(2) \\A_(T)=135 m^(2)`

Have a great day

Answer 2

D. 135 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The first diagonal is

9m+6m=15m

Note that the vertical diagonal is the axis of symmetry of the kite.

This diagonal bisect the kite

Therefore the second diagonal is

2(9m)=18m

The area of the kite

`= (1)/(2) * 18 * 15`

`= 9 * 15`

`= 135 {m}^(2)`