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;
[tex]A = \frac{s^2 \times n}{4 \times \tan(\frac{180}{n})}[/tex] ......[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];
[tex]6.9 =\frac{s^2 \times 5}{4 \times \tan(\frac{180}{5})}[/tex]
or
[tex]6.9 = \frac{s^2 \times 5}{4 \times \tan(36)}[/tex]
or
[tex]6.9 \times 4 \times \tan(36)= s^2 \times 5[/tex]
[tex]s^2 =\frac{6.9 \times 4 \times \tan(36)}{5}[/tex]
Taking both side square root, we have;
[tex]s=\sqrt{\frac{6.9 \times 4 \times \tan(36)}{5}}[/tex]
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) = [tex]5 \times s[/tex] where s is the side.
Substitute the value of s≈ 2.00 cm.
P = [tex]5 \times 2.00 = 10[/tex] cm
therefore, the perimeter of the regular pentagon is; 10 cm
