Question

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is `3`, its base's sides have lengths of `7`, and its base has a corner with an angle of `(5 pi)/6`. What is the pyramid's surface area?

Answer 1

`color(purple)(A_p = A_b + L S A = 24.5 + 64.54 = 89.04` sq units

Explanation:

Pyramid’s Surface Area `A_p = A_b + L S A`

where `A_b = s^2 sin theta, L S A = 4 * (1/2) s sqrt((s/2)^2 + h^2)`

Given `s = 7, h = 3, theta = (5pi)/6`

`A_b = 7^2 * sin ((5pi)/6) = 24.5`

`L S A = 4 * (1/2) *7 * sqrt((7/2)^2 + 3^2) ~~ 64.54`

`color(purple)(A_p = A_b + L S A = 24.5 + 64.54 = 89.04` sq units