Question

36 Find the surface area. The apothem is 3.464 cm.

4 cm
A.
B.
C. 196 cm²
D. 288 cm²
144 cm²
185.6 cm²
12 cm

Answer 1

we have a hexagonal pyramid above, hmmm it has six triangles, each with a base of 4 and a height of 12, and a hexagonal base with an apothem of 3.464 and sides of 4.

`\textit{area of a regular polygon}\\\\ A=\cfrac{ap}{2} ~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3.464\\ p=\stackrel{6* 4}{24} \end{cases}\implies A=\cfrac{(3.464)(24)}{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{six triangles}}{6\left[\cfrac{1}{2}(\underset{b}{4})(\underset{h}{12}) \right]}~~ + ~~\stackrel{ hexagon }{\cfrac{(3.464)(24)}{2}}}\implies 144+41.568 ~~ \approx ~~ \text{\LARGE 185.6}~cm^2`