A regular pentagon has an apothem of 7.43 centimeters. Find the length of a side of the pentagon and the length of the radius of the circumscribed circle

By definition, the apothem of a pentagon is given by the following mathematical formula:

ap = ((L) / (1.45))

Where

ap: apotema

L = side.

The length of a side of the pentagon is

L = (ap) * (1.45)

Substituting

L = (7.43) * (1.45) = 10.77 cm

The radius of the circumscribed circle can be found by the Pythagorean

theorem in the following way:

r = root ((L / 2) ^ 2 + (ap) ^ 2)

substituting

r = root ((10.77 / 2) ^ 2 + (7.43) ^ 2) = 9.17 cm

answer:

L = 10.77 cm

r = 9.17 cm