Question

Plzzz help of your good in math

Answer 1

Answer: 117.45 ft²

Explanation:

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

`SA=(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=(1)/(2)*perimeter*apothem=(1)/(2)*24ft*2√(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:

`(4ft)/(2)=2ft`

Then:

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

Then, the surface area is:

`SA=(1)/(2)(24ft)(2√(10)ft)+(41.56ft^(2))=117.45ft^(2)`