Question

Find the total area (in terms of K) of the prism. Place "K" last in your formula. T.A. =

Answer 1

Assuming that the base of the prism is a regular pentagon, the area of a regular polygon is given by the formula A = 0.5pa; where p is the perimeter and a is the apothem. An apothem is a line that connects the center of the polygon to the midpoint of a side and is also perpendicular to the said side. For this example, the assumed apothem here is k.

Area of base = 2 (0.5 x 20" x k) = 20k

The sides of the prism are rectangles, with width 6" and length (20"/5) = 4".
Area of sides of prism = 5 (6" x 4") = 120

Total Area T.A. = 120 + 20k

Answer 2

Area of base = 2 (0.5 x 20" x k) = 20k

The sides of the prism are rectangles, with width 6" and length (20"/5) = 4".

Area of sides of prism = 5 (6" x 4") = 120

Total Area T.A. = (120 + 20k)

This is correct because I did this question and got it right.