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