Question

The surface area of a square pyramid is 84 square inches. The side length of the base is 6 inches. What is the value of x?

Answer 1

x= 4 inches

Explanation:

Surface Area Of A Square Pyramid

It can be computed by adding the area of the base plus 4 times the area of the sides. The area of the base (a square) is

`\displaystyle A_b=L^2=36\ in^2`

The area of each lateral side (a triangle) is

`\displaystyle A_s=(1)/(2)LX=(1)/(2)(6)x=3X`

The total area of the pyramid is

`\displaystyle A_b+4A_S`

It must be equal to 84, so

`\displaystyle 36+4(3X)=84`

`\displaystyle 12X=48`

Solving for x

`\boxed{\displaystyle X=4\ in}`