Question

Square pyramid is made up of a base with a side length of 10 inches and faces that are triangles with a height of 12 inches what is the surface area of the square pyramid

Answer 1

The surface area of the square pyramid is 360 in²

Explanation:

Given that the side length is 10 inches.

The height of the pyramid is 12 inches.

We need to determine the surface area of the pyramid.

The surface area of the pyramid is given by

$SA=s^2+2sl$

Where s is the side length and l is the slant height.

The slant height can be determined using the formula,

$l=\sqrt{h^2+b^2}$

where h = 12 and $b=\frac{s}{2} =5$

Substituting these values in the formula, we get,

$l=\sqrt{12^2+5^2}$

 $=\sqrt{144+25}$

$l=\sqrt{169}$

$l=13$

Thus, the slant height is $l=13$

Now, we shall find the surface area of the pyramid.

Substituting $l=13$ and $s=10$ in the formula $SA=s^2+2sl$, we get,

$SA=10^2+2(10)(13)$

     $=100+260$

$SA=360 \ in^2$

Thus, the surface area of the square pyramid is 360 in²