Question

The base of a square pyramid that has a slant height of 37 and a height of 35 is what? Use miles as your label.

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{35} \end{cases} \\\\\\ x=√( 37^2 - 35^2)\implies x=√( 1369 - 1225 ) \implies x=√( 144 )\implies x=12 \\\\[-0.35em] ~\dotfill\\\\ (2x)(2x)\implies (24)(24)\implies \stackrel{ \textit{ base} }{\text{\LARGE 576}}~mi^2`