Question

Trapezium Pythagoras ...................................

Answer 1

Check the picture below.

so let's find its height "h"

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=√(c^2 - a^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=√( 17^2 - 8^2)\implies h=√( 289 - 64 ) \implies h=√( 225 )\implies h=15 \\\\[-0.35em] ~\dotfill`

`\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\\ a=12\\ b=20\\ h=15 \end{cases}\implies A=\cfrac{15(12+20)}{2} \\\\\\ A=\cfrac{15\cdot 32}{2}\implies A=(15)(16)\implies A=240~m^2`

since one can covers 100 m², and we need to cover 240 m², so we'd need three cans then, that'd be (3)(19.75) = 59.25.