Question

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 cm2

plz dont ask for a pic i cant put one

Answer 1

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)

Answer 2

`\text{Hence, area of regular pentagon is }32.7 cm^2`

Explanation:

Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

we have to find the area of pentagon.

Apothem=a=3 cm

Perimeter=s=21.8 cm

`\text{Area of regular pentagon=}(1)/(2)* apothem* perimeter`

`(1)/(2)* s * a`

`=(1)/(2)* 21.8* 3`

`=(65.4)/(2)=32.7 cm^2`

`\text{Hence, area of regular pentagon is }32.7 cm^2`

Option 3 is correct.