Question

Need help with geometry

Answer 1

Answer:

The surface area is $305.9\ ft^{2}$

Step-by-step explanation:

we know that

The surface area of the square pyramid is equal to

$SA=b^{2}+4[\frac{1}{2}bh]$

where

b is the length side of the square base

h is the height of the lateral triangular face

we have

$b=10\ ft$

Applying Pythagoras Theorem find the value of h

$h^{2}=9^{2}+(10/2)^{2}$

$h^{2}=81+25$

$h=\sqrt{106}\ ft$

substitute in the formula

$SA=10^{2}+4[\frac{1}{2}(10)(\sqrt{106})]=305.9\ ft^{2}$