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

Answer:

Option C is correct.

The perimeter of the regular pentagon is, 10 cm

Step-by-step explanation:

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

$A = \frac{s^2 \times n}{4 \times \tan(\frac{180}{n})}$  ......[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];

$6.9 =\frac{s^2 \times 5}{4 \times \tan(\frac{180}{5})}$

or

$6.9 = \frac{s^2 \times 5}{4 \times \tan(36)}$

or

$6.9 \times 4 \times \tan(36)= s^2 \times 5$

$s^2 =\frac{6.9 \times 4 \times \tan(36)}{5}$

Taking both side square root, we have;

$s=\sqrt{\frac{6.9 \times 4 \times \tan(36)}{5}}$

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) = $5 \times s$ where s is the side.

Substitute the value of s≈ 2.00 cm.

P = $5 \times 2.00 = 10$ cm

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