Question

The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm

Answer 1

The answer is C. 10cm

Answer 2

Given

Area of the regular pentagon is 6.9 cm².

Find out the perimeter of a regular pentagon

To proof

Formula

Area of regular pentagon is

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

As given in the question

area of regular pentagon = 6.9 cm²

now equating the area value with the area formula.

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

Now put

√5 = 2.24 ( approx)

put in the above equation

$\frac{6.9\times 4}{\sqrt{5(5+2\times2.24)}}=a^{2}\\\frac{27.6}{\sqrt{47.4}}=a^{2}\\\frac{27.6}{6.88}=a^{2}$

thus

a² = 4.01

a = √ 4.01

a = 2.0 cm ( approx)

As perimeter  represented the sum of all sides.

i.e regular pentagon have five sides of equal length.

Thus

perimeter of the regular pentagon = 5 × side length

                                                         = 5 ×2.00

therefore the perimeter of the regular pentagon = 10cm

option c is correct

Hence proved