Plzzz help of your good in math

Accepted Solution

Answer: 117.45 ft²Step-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]