The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm
2 answers:
As the regular pentagon there is 5 regular triangles.
And the area of 1 regular triangle is:
At = Side^2 × √(3)/4
But, as the pentagon has 5 triangle
Then,
Ap = 5 × Side^2 . √(3)/4
Replacing Ap = 6.9
5 × Side^2 . √(3)/4 = 6.9
Side^2 . √(3)/4 = 6.9 ÷ 5
Side^2 . √(3) = 4 × 1,38
Side^2 = 5,52 ÷ √(3)
Side^2 = 3,187
Side = √(3,187)
Side = 1,785 cm
Then,
The total perimeter will be:
P = 5 × Side
P = 5 × 1,785
P = 8,92 cm
Well, I did find this answer.
we know that
The formula to find the area of a regular polygon is given by
where
s is the length of the side
n is the number of sides
In this problem we have
Solve for S
<u>Find the length of the side of the regular pentagon</u>
<u>Find the perimeter of the regular pentagon</u>
therefore
<u>the answer is </u>
the perimeter of the regular pentagon is
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