# Math Help - The height of a pyramid

1. ## The height of a pyramid

The square base of a regular pyramid has a side length of 4. Each of the other 4 faces of the pyramid is a triangle with a base of 4 and a height of 6. The pyramid has a total surface area of 64. A second regular pyramid has a square base that is 4 by 4 but its total sure area is double that of the first pyramid. What is the height of each of the triangular faces of the second pyramid?

I know that the answer is 14, but is there a way to find this without knowing the formula (1/2 (p)(l) + B = TSA)? It's a practice standardized test question

2. ## Re: The height of a pyramid

You have one square + 4 triangles that make the surface area.

$L^2 + 4 \times \frac{1}{2} \times b \times h = 128$

We know the information about the base which is also the length of the square so

$4^2 + 4 \times \frac{1}{2} \times 4 \times h = 128$

$16 + 8 \times h = 128$

solve for $h$