The square base of a pyramid has an area of 144 square feet. If the slant height of the pyramid is 10 feet, what is the height of the pyramid

Answer 1

the height of the pyramid goes from the apex (top vertex) to the center of the base

the distance from the center of the base to the slant height at the base edge is 6 feet because the square base has an area of 144 square feet and therefore each edge of the square base is 12 feet (12*12=144)

the height h, the slant height 10, and the segment 6 from the center to the edge form a right triangle

using the Pythagorean Theorem

h^2+6^2=10^2

h^2+36=100

h^2=100-36

h^2=64

h=√64

h=8 feet for the height of the pyramid

Answer 2

a² + b² = c²

 

A_square = s² (Area of a square is the length of its side... squared)

A = 144

144 = s²

12 = s

So the length of a side of the base is 12 ft.

12/2 = 6 (the halfway spot is 6, which leads to right below the top of the pyramid, to form the right triangle)

 

6² + b² = 10²

36 + b² = 100

b² = 64

b = 8