Question

The area of the regular pentagon is 6.9 cm2.

What is the perimeter?

Answer 1

I think its 10.01cm

I hope this helps ^-^
let me know if im wrong

Answer 2

Area of a regular pentagon(A) is given by:

`A=(1)/(4)(\sqrt{5(5+2√(5)}) s^2`

where, s is the side of the regular pentagon

As per the statement:

The area of the regular pentagon is 6.9 cm^2.

⇒A = 6.9 cm^2

then;

`6.9=(1)/(4)(\sqrt{5(5+2√(5)}) s^2`

Multiply both sides by 4 we have;

`27.6=\sqrt{5(5+2√(5)}s^2`

Simplify:

`27.6 = √(47.3606798)s^2`

⇒
`27.6 = √(47.3606798)s^2`

Divide both sides by
`√(47.3606798)` we have;

`4.01051475= s^2`

⇒
`√(4.01051475)=s`

⇒2.00262696 cm = s

or

s = 2.00262696 cm

Perimeter of the regular pentagon(P) is given by:

`P=5s`

then;

`P = 5 \cdot 2.00262696 = 10.0131348 cm`

Therefore, the perimeter is, 10.0131348 cm