Question

Please please please help me. I have no idea what to do

Answer 1

We have a bunch of rectangles making up the lateral sides of this figure. They have side length 12 and height 13.

So the area of one rectangle is 12 x 13 = 156.
We have 6 of these rectangles, so our lateral area is 6(156) = 936.

The total surface area requires that we include the area of the base. To find the area of a regular polygon we take half of the product of the apothem and perimeter.

A = (1/2)*a*p

The apothem is given to be 10.39,
and the perimeter is fairly easy to calculate:
With the side length being 12, the perimeter is then 6(12) = 72.

So then the area of our base is (1/2)*10.39*72 = 374.04

So then the total surface area is the (base area) + (lateral area),
374.04 + 936 = 1310.04