Question

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29 inches

Answer 1

For solving of the area of a square pyramid, we can use the formula below:
A=a²+2a sqrt (a²/4 +h²)
where s for the slant height, r for the a/2, where a is the side length and h for the height
Substitute the values, 
A=40²+(2*40) SQRT (40²/4 +21²)
A=3920
The answer is 3920 for the area of the square pyramid.

Answer 2

Answer with explanation:

Base of Pyramid which is in the shape of square ,having length of each side =40 inches

Height of pyramid = 21 inches

Slant height = 29 inches

Surface area of Square Pyramid

= Area of four Triangular faces +Area of Square base

 Relation between Slant height (S), Length of base (B) and Height (H) of pyramid

 $S=\frac{\sqrt{B^2+4H^2}}{2}$

$29^2=\sqrt{\frac{40^2}{4}+21^2}$

So,this is a Square pyramid.

Surface area of Pyramid

      $=B\times(B+2 S)\\\\=B \times(B+\sqrt{B^2+4H^2})\\\\=40 \times(40+\sqrt{40^2+4\times 21^2})\\\\=40 \times(40+\sqrt{3364})\\\\=40 \times(40+58)\\\\=40 \times 98\\\\=3920$ square inches

Volume of Pyramid

 $=\frac{1\times a^2\times H}{3}\\\\=\frac{40^2 \times 21}{3}\\\\=1600 \times 7\\\\=11200$ cubic inches