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Nuetrik [128]
3 years ago
8

PLEASE ANSWER WITH AN EXPLANATION! THANK YOU

Mathematics
1 answer:
lubasha [3.4K]3 years ago
8 0

Answer:

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

Step-by-step explanation:

<em>Look at the picture.</em>

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

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