Question

a right - square pyramid has a surface area of 75264 square inches which includes a base area of 36864 square inches. what is the slant height, in inches, of this pyramid?

Explanation:

Step1: Find lateral - surface area

$75264 - 36864=38400$ (square inches)

Step2: Find side - length of base

Since base area $A = s^{2}=36864$, then $s=\sqrt{36864}=192$ inches.

Step3: Use lateral - area formula

Lateral - area of square pyramid $L = 2sl$. So $l=\frac{L}{2s}$. Substitute $L = 38400$ and $s = 192$, we get $l=\frac{38400}{2\times192}=100$ inches.

Answer:

100