Question

Plzzz help of your good in math

Answer 1

Answer: 117.45 ft²

Step-by-step explanation:

There is a general formula for calculate the surface area of a regular pyramid. This is:

$SA=\frac{1}{2}p*l+B$

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

The perimeter is:

$P=6(4ft)=24ft$

The base is an hexagon, therefore you can find the area by using the formula for the area of a regular polygon:

$B=\frac{1}{2}*perimeter*apothem=\frac{1}{2}*24ft*2\sqrt{3}ft=41.56ft^{2}$

The slant height can be calculated with Pythagorean theorem. The hypotenuse is the slant height and the other legs are 6ft and:

$\frac{4ft}{2}=2ft$

Then:

$l=\sqrt{(6ft)^{2}+(2ft)^{2}}=2\sqrt{10}ft$

  Then, the surface area is:

$SA=\frac{1}{2}(24ft)(2\sqrt{10}ft)+(41.56ft^{2})=117.45ft^{2}$