Find the area of a pentagon with an apothem of 5 units. round to the nearest hundredth

The area of a pentagon is given by:

A = (5 * L * ap) / 2

Where,

L: length of the sides

ap: apothem

Then, L in function of the apothem is given by:

L = 2 * tan (theta / 2) * ap

Where,

theta: central angle

Substituting:

A = (5 * (2 * tan (theta / 2) * ap) * ap) / 2

A = (5 * (2 * tan (72/2) * 5) * 5) / 2

A = (5 * (2 * tan (36) * 5) * 5) / 2

A = 90.82 units ^ 2

Answer:

the area of a pentagon with an apothem of 5 units is:

A = 90.82 units ^ 2