Question

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

Answer 1

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