Question

find the surface area of the pyramid SA= __ in squared. do not round until final answer. then round to the nearest whole number as needed.

Answer 1

$\begin{equation*} 851\:m^2 \end{equation*}$

1) Since we need to find the Surface Area of that Pyramid, we need to examine that picture. We can see that there are 6 triangles in this pyramid. And the base is formed by a hexagon.

2) Let's then find the Lateral Area:

$L__{Area}=6(\frac{16\cdot16}{2})=768m^2$

Since at the base of that pyramid, there is a regular hexagon we can subdivide this into 6 triangles.

$\begin{gathered} B=6(\frac{16\sqrt{3}}{2}) \\ B=3\cdot16\sqrt{3} \\ B=48\sqrt{3} \end{gathered}$

3) Now, we can add them up:

$\begin{gathered} TSA=768+48\sqrt{3} \\ TSA=48\left(16+\sqrt{3}\right)\approx851\:m^2 \end{gathered}$

Note that we rounded off to the nearest whole number as requested.