Question

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

Answer 1

10
random words to fill up 20 character minimum for answering questions :P

Answer 2

Option C is correct.

The perimeter of the regular pentagon is, 10 cm

Explanation:

The formula for the area of n-sided regular polygon is given by;

`A = (s^2 * n)/(4 * \tan((180)/(n)))` ......[1]; where s is the length of the side and n is the number of side .

Given: Area of regular pentagon is 6.9 square cm.

Here, n =5

to find s;

Substitute the value of A and n in equation [1];

`6.9 =(s^2 * 5)/(4 * \tan((180)/(5)))`

or

`6.9 = (s^2 * 5)/(4 * \tan(36))`

or

`6.9 * 4 * \tan(36)= s^2 * 5`

`s^2 =(6.9 * 4 * \tan(36))/(5)`

Taking both side square root, we have;

`s=\sqrt{(6.9 * 4 * \tan(36))/(5)}`

Simplify:

s = 2.00263 cm

or

s ≈ 2.00 cm

Therefore, the side of the length of regular pentagon is, s≈ 2.00 cm

Now, to find the perimeter of regular pentagon;

Use the formula:

Perimeter of regular pentagon(P) =
`5 * s` where s is the side.

Substitute the value of s≈ 2.00 cm.

P =
`5 * 2.00 = 10` cm

therefore, the perimeter of the regular pentagon is; 10 cm