Question

PLEASE ANSWER WITH AN EXPLANATION! THANK YOU

Answer 1

Answer:

$\large\boxed{A=153\ cm^2}$

Step-by-step explanation:

Look at the picture.

We have

square with side length a = 9

trapezoid with base lengths b₁ = 9 and b₂ = 6 and the height length h = 6

right triangle with legs lengths l₁ = 3 + 6 = 9 and l₂ = 6

The formula of an area of a square

$A=a^2$

Substitute:

$A_I=9^2=81\ cm^2$

The formula of an area of a trapezoid:

$A=\dfrac{b_1+b_2}{2}\cdot h$

Substitute:

$A_{II}=\dfrac{9+6}{2}\cdot6=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2$

The formula of an area of a right triangle:

$A=\dfrac{l_1l_2}{2}$

Substitute:

$A_{III}=\dfrac{(9)(6)}{2}=\dfrac{54}{2}=27\ cm^2$

The area of the shape:

$A=A_I+A_{II}+A_{III}\\\\A=81+45+27=153\ cm^2$