A square pyramid and a cube have the same surface area. The length of each side of the base of the square pyramid is 10 feet. The width of the cube is 6 feet. What is the slant height of the square pyramid?

The answer to your question is 23.2 ft

Step-by-step explanation:

Data

length square pyramid = 10 ft

width of a cube = 6 ft

height of the pyramid = ?

The surface area is equal in both figures.

Formula

Surface area of a cube = 6a²

Surface area of a square pyramid = ab + al = l x l + (l x h) / 2

Process

1. - Calculate the surface area of the cube

Ac = 6 (6) ² = 6 (36)

= 216 ft²

2. - Substitute data in the square pyramid formula

Ap = (10 x 10) + (10h) / 2

3. - Equal both areas

216 = 100 + 5h

- Solve for h

216 - 100 = 5h

116 = 5h

h = 116 / 5

- Result

h = 23.2 ft