Q:

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2plz dont ask for a pic i cant put one

Accepted Solution

A:
Answer:
n = 5
a = 4.35926 cm
r = 3 cm
R = 3.7082 cm
A = 32.6944 cm²= 32.7 cm²
P = 21.7963 cm
x = 108 °
y = 72 °

Agenda:
r = inradius (apothem)
R = circumradius 
a = side length
n = number of sides
x = interior angle
y = exterior angle 
A = area
P = perimeter
π = pi = 3.14159...
√ = square root

Formula:

Inradius r = (1/2)a cot(π/n) = R cos(π/n)