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