Question

PLEASE HELP ME
What is the area and perimeter of the figure?
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Answer 1

Check the picture below.

so its area is the area of a triangle and two rectangles.

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{12})(\underset{h}{5})}~~ + ~~\stackrel{rectangle}{(15)(2)}~~ + ~~\stackrel{rectangle}{(3)(5)}}\implies 30+30+15\implies \text{\LARGE 75}`

now, for the perimeter, let's find the length of the slanted line.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=b^2+h^2\implies c=√(b^2 + h^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ b=\stackrel{adjacent}{12}\\ h=\stackrel{opposite}{5} \end{cases} \\\\\\ c=√( 12^2 + 5^2)\implies c=√( 144 + 25 ) \implies c=√( 169 )\implies c=13 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{13+2+15+7\implies \text{\LARGE 37}}`