Find the area of a regular pentagon with a side length of 14 and an apothem of 22.

The main area formula is A = 5x s x r / 2

where s is a side

r is the radius, r can be found as following

r is the hypothenuse, so tanα=a/S, where S=s/2=7

tanα=22/7=Pi, so α=arctanPi = 72.3°

for finding r, r = a/sin α=22/sin 72.3°=23

so finally

the area is A = (5x 14x 23) / 2=808