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ANSWER

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

[tex] = \frac{1}{2} \times 18 \times 15[/tex]

[tex] = 9 \times 15[/tex]

[tex] = 135 {m}^{2} [/tex]

Answer:

[tex]A_{T}=135 m^{2[/tex]

Step-by-step 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)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{1} =40.5\ m^{2}[/tex]

Step 2

triangle 2 (RIGHT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{2} =40.5\ m^{2}[/tex]

Step 3

triangle 3 (LEFT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{3} =27\ m^{2}[/tex]

Step 4

triangle 4 (RIGHT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{4} =27\ m^{2}[/tex]

Step 5

Total Area

the total area is

[tex]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}[/tex]

Have a great day

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