Question

These two trapeziums are similar.

Calculate the area of trapezium G.
If your answer is a decimal, give it to 1 d.p.

Answer 1

Check the picture below.

so let's firstly get the corresponding side of "a".

`\textit{Area of a Trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=5\\ b=16\\ A=70 \end{cases} \implies 70=\cfrac{5(a+16)}{2} \\\\\\ 140=5(a+16)\implies \cfrac{140}{5}=a+16\implies 28=a+16\implies 12=a \\\\[-0.35em] ~\dotfill`

`\cfrac{12^2}{30^2}~~ = ~~\cfrac{70}{A}\implies \left( \cfrac{12}{30} \right)^2 =\cfrac{70}{A}\implies \left( \cfrac{2}{5} \right)^2=\cfrac{70}{A}\implies \cfrac{4}{25}=\cfrac{70}{A} \\\\\\ 4A=1750\implies A=\cfrac{1750}{4}\implies \boxed{A=437.5~cm^2}`