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. What is the surface area of the pyramid? 3,280 inches 3,280 square inches 3,920 inches 3,920 square inches

Answer 1

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

Answer 2

Answer    

Find out the  what is the surface area of the pyramid .

To proof

Formula

Surface area of a square pyramid

$= a^{2} + 2a \sqrt{\frac{a^{2}}{4} +h^{2}$

Where a is the base edge and h be the height .

As given

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.

i.e Base edge = 40 inches

Height =  21 inches    

Put values in the above formula

$= 40^{2} + 2\times40\times\sqrt{\frac{40^{2}}{4} +21^{2}$

solving

$= 1600 + 80 \sqrt{\frac{1600}{4} + 441$

$= 1600 + 80\times\sqrt{841}$

$\sqrt{841} = 29$

= 1600 + 80 × 29

= 3920 inches²

Therefore the surface area of the pyramid is 3,920 inches²

Hence proved