Question

what is the lateral surface area of the equilateral triangular pyramid below?

Answer 1

$\text{area}=192ft^2$

Explanation

as we can see we have 4 similar triangles, let

$\begin{gathered} \text{area}=4\text{ times area of a triangle} \\ \end{gathered}$

then,Let

base=12 ft

height=8 ft

the area of a triangle is given by:

$\begin{gathered} \text{Area}_{triangle}=\frac{base\cdot heigth}{2} \\ \text{replace}, \\ \text{area}=4\text{ times area of a triangle} \\ \text{area}=4\text{(}\frac{base\cdot\text{height}}{2}) \\ \text{area=}4\text{ (}\frac{12\text{ ft}\cdot8\text{ ft}}{2}) \\ \text{area}=4(\frac{96}{2}ft^2) \\ \text{area}=192ft^2 \end{gathered}$