Question

What is the area of a regular pentagon with a side length of 9 millimeters and an apothem length of 6.2 millimeters?

Answer 1

The area of a regular polygon is equal to half of the product of its apothem and perimeter.
                           A = 0.5aP

Find first the perimeter,
                          P = 5 x (9 mm)
                           P = 45 mm

Substituting the perimeter and the apothem to the first equation,
                         A = 0.5(45 mm)(6.2 mm)
                          A = 139.5 mm²

Therefore, the area of the regular pentagon is equal to 139.5 mm².