# The height of a pyramid

• Aug 24th 2011, 11:24 AM
mjoshua
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 :(
• Aug 24th 2011, 01:52 PM
pickslides
Re: The height of a pyramid
You have one square + 4 triangles that make the surface area.

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

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

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

$\displaystyle 16 + 8 \times h = 128$

solve for $\displaystyle h$