Question

The triangular pyramid has identical equilateral triangles as its faces. Find the surface area of the pyramid.

Alternative Text

A. 113.4 ft2
B. 140.4 ft2
C. 226.8 ft2
D. 631.8 ft2

Answer 1

B. 140.4 square feet.

Explanation:

If all faces are equilateral, and they are all congruent, that means the surface area of the pyramid is formed by 4 equal triangles, including the base.

We just need to find the area of one triangle and then multiply it by 4.

According to the image, the height of a triangle face is
`h=7.8 \ ft`, and its base is
`b=9 \ ft`. So, the area is

`A=(1)/(2) (b * h)`

`A=(1)/(2)(7.8 * 9) =35.1 \ ft^(2)`

Then, the total surface area of the pyramid is

`S=4(35.1)=140.4 \ ft^(2)`

Therefore, the right answer is B. 140.4 square feet.