Answer: 117.45 ft²
Step-by-step explanation:
There is a general formula for calculate the surface area of a regular pyramid. This is:
[tex]SA=\frac{1}{2}p*l+B[/tex]
Where p is the perimeter of the base, l is the slant height and B is the area of the base.
The perimeter is:
[tex]P=6(4ft)=24ft[/tex]
The base is an hexagon, therefore you can find the area by using the formula for the area of a regular polygon:
[tex]B=\frac{1}{2}*perimeter*apothem=\frac{1}{2}*24ft*2\sqrt{3}ft=41.56ft^{2}[/tex]
The slant height can be calculated with Pythagorean theorem. The hypotenuse is the slant height and the other legs are 6ft and:
[tex]\frac{4ft}{2}=2ft[/tex]
Then:
[tex]l=\sqrt{(6ft)^{2}+(2ft)^{2}}=2\sqrt{10}ft[/tex]
Then, the surface area is:
[tex]SA=\frac{1}{2}(24ft)(2\sqrt{10}ft)+(41.56ft^{2})=117.45ft^{2}[/tex]
