Question

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

Answer 1

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