Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5.

The area of the triangle is 1/2 base times height.

To find the surface area of the Pentagon you need to divide it up into five triangles, the side length is eight and the height in the triangle inside the Pentagon is 5.5. The formula for The area of the triangle is 1/2 base times height. The base this is eight. Area of one of the five triangles = 1/2*8*5.5 = 22. There are 5 triangle in one side of pentagon prism so you need to times 22*5 = 110. Since there are two pentagons [the top one and the bottom one you time this by 2 = 220. Now we need to find the area of 5 rectangles that form the sides. Area of a rectangle is length time width ... the length 8 and the width is 20 = 160 for one rectangle. There are 5 rectangles ... 160 times 5 = 800. Put them all together and you get 800+220 = 1020 sq feet