Question

Find the area of a regular pentagon with radius 3cm. Round to the nearest tenth.

No picture is given, but I believe a circle can surround the figure. I'm not really sure how to find the area of the figure when the side length isn't given. Can you guys help me?

Thanks much!

Answer 1

if it fits inside the circle, the distance from the center to a point of the pentagon is 3 cm.
There are five isoceles triangles in the pentagon, each with an angle at the center of 360/5 = 72 degrees and sides of 3 cm
What we have to do is find the area of that triangle and multiply by 5
we need the base of the triangle and its altitude
look at right triangle formed by altitude and base
72/2 = 36 degrees
hypotenuse = 3
so altitude /3 = cos 36
half base/3 = sin 36
altitude = 2.43
half base = 1.76
area of isoceles triangle = half base * altitude = 4.28
5 times triangle area = 21.4
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rough check (credit Archimedes)
area of circle around it = pi (3)^2 = 28.3 so or answer is not crazy