Question

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

Answer 1

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

Step-by-step 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)=(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((96)/(2)ft^2) \\ \text{area}=192ft^2 \end{gathered}`