Question

Type the correct answer in the box. Use numerals instead of words.What is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet?The total surface area is aboutsquare feet

Answer 1

The surface area of an equilateral triangular pyramid is given by:

$SA=B+3AL$

Where:

$B=\frac{\sqrt[]{3}}{4}l^2=\frac{\sqrt[]{3}}{4}(6)^2=9\sqrt[]{3}$$\begin{gathered} AL=\frac{6\cdot(\sqrt[]{3^2+10^2})}{2} \\ AL=3\sqrt[]{109} \end{gathered}$

So:

$\begin{gathered} SA=9\sqrt[]{3}+3(3\sqrt[]{109}) \\ SA=9\sqrt[]{3}+9\sqrt[]{109} \\ SA\approx110ft^2 \end{gathered}$

Answer:

110