Question

100 POINTS HELP ME PLZZ

Answer 1

`\displaystyle \Large \boxed{\sf 720 \ in^2}`

Explanation:

Use formula to calculate area of trapezium

`\displaystyle A=(\left(a+b\right)\cdot h)/(2)`

Substitute the values and evaluate

`\displaystyle A=(\left(24+36\right)\cdot 24)/(2)=720`

Answer 2

720 in²

Explanation:

The composite figure is made up of a triangle and a square.

Area of the triangle

`\boxed{\begin{aligned}\textsf{Area of a triangle}&=(1)/(2) * \sf base * height\\\\ \implies \textsf{Area of triangle}&=(1)/(2) * (36-24) * 24\\&=(1)/(2) * 12 * 24\\&=6 * 24\\&=144\; \sf in^2\end{aligned}}`

Area of the square

`\boxed{\begin{aligned}\textsf{Area of a square}&=\sf side\; length * side\; length\\\\ \implies \textsf{Area of the square}&= 24 * 24 \\&=576\; \sf in^2\end{aligned}}`

Therefore, the area of the composite figure is:

`\boxed{\begin{aligned}\textsf{Area of the composite figure}&=\sf Triangle + Square\\ & = 144+ 576\\&=720\; \sf in^2\end{aligned}}`