Question

The diagram below is a representation of a soccer goal.

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=h^2\implies o=√(h^2 - a^2) \end{array} \qquad \begin{cases} h=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{3.5}\\ o=\stackrel{opposite}{c} \end{cases} \\\\\\ c=√( 8^2 - 3.5^2)\implies c=√( 64 - 12.25 ) \implies c=√( 51.75 )\implies \boxed{c\approx 7.2~ft} \\\\[-0.35em] ~\dotfill`

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\underset{b}{3.5})(\underset{h}{7.2}) \right]}~~ + ~~\stackrel{ rectangle }{(12)(7.2)}} ~~ \approx ~~\stackrel{ \textit{nettting to cover to soccer goal} }{25.2+ 86.4~~ \approx ~~\text{\LARGE 111.6}~ft^2}`