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

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=(√(B^2+4H^2))/(2)`

`29^2=\sqrt{(40^2)/(4)+21^2}`

So,this is a Square pyramid.

Surface area of Pyramid

`=B*(B+2 S)\\\\=B *(B+√(B^2+4H^2))\\\\=40 *(40+√(40^2+4* 21^2))\\\\=40 *(40+√(3364))\\\\=40 *(40+58)\\\\=40 * 98\\\\=3920` square inches

Volume of Pyramid

`=(1* a^2* H)/(3)\\\\=(40^2 * 21)/(3)\\\\=1600 * 7\\\\=11200` cubic inches

Answer 2

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.