Question

PLEASE ANSWER WITH AN EXPLANATION! THANK YOU

Answer 1

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

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=(b_1+b_2)/(2)\cdot h`

Substitute:

`A_(II)=(9+6)/(2)\cdot6=(15)/(2\!\!\!\!\diagup_1)\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2`

The formula of an area of a right triangle:

`A=(l_1l_2)/(2)`

Substitute:

`A_(III)=((9)(6))/(2)=(54)/(2)=27\ cm^2`

The area of the shape:

`A=A_I+A_(II)+A_(III)\\\\A=81+45+27=153\ cm^2`