Answer:
The surface area is [tex]305.9\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the square pyramid is equal to
[tex]SA=b^{2}+4[\frac{1}{2}bh][/tex]
where
b is the length side of the square base
h is the height of the lateral triangular face
we have
[tex]b=10\ ft[/tex]
Applying Pythagoras Theorem find the value of h
[tex]h^{2}=9^{2}+(10/2)^{2}[/tex]
[tex]h^{2}=81+25[/tex]
[tex]h=\sqrt{106}\ ft[/tex]
substitute in the formula
[tex]SA=10^{2}+4[\frac{1}{2}(10)(\sqrt{106})]=305.9\ ft^{2}[/tex]
