Answer:
[tex]\large\boxed{A=153\ cm^2}[/tex]
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
[tex]A=a^2[/tex]
Substitute:
[tex]A_I=9^2=81\ cm^2[/tex]
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
Substitute:
[tex]A_{II}=\dfrac{9+6}{2}\cdot6=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2[/tex]
The formula of an area of a right triangle:
[tex]A=\dfrac{l_1l_2}{2}[/tex]
Substitute:
[tex]A_{III}=\dfrac{(9)(6)}{2}=\dfrac{54}{2}=27\ cm^2[/tex]
The area of the shape:
[tex]A=A_I+A_{II}+A_{III}\\\\A=81+45+27=153\ cm^2[/tex]
