Answer:
[tex]72\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the square pyramid is equal to the area of the square base plus the area of its four lateral triangular faces
so
[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 triangular face
Remember that
Each lateral triangular face is a triangle 45°-90°-45°
so
[tex]h=b/2[/tex]
we have
[tex]b=6\ ft[/tex]
so
[tex]h=6/2=3\ ft[/tex]
substitute in the formula
[tex]SA=6^{2}+4[\frac{1}{2}(6)(3)]=72\ ft^{2}[/tex]
