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

Answer:

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

$A=\frac{1}{4}(\sqrt{5(5+2\sqrt{5}}) s^2$

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;

$6.9=\frac{1}{4}(\sqrt{5(5+2\sqrt{5}}) s^2$

Multiply both sides by 4 we have;

$27.6=\sqrt{5(5+2\sqrt{5}}s^2$

Simplify:

$27.6 = \sqrt{47.3606798}s^2$

⇒$27.6 = \sqrt{47.3606798}s^2$

Divide both sides by $\sqrt{47.3606798}$  we have;

$4.01051475= s^2$

⇒$\sqrt{4.01051475}=s$

⇒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