Posted by **Nikki** on Saturday, April 19, 2008 at 4:18pm.

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!

- Geometry -
**Damon**, Saturday, April 19, 2008 at 6:26pm
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

===============================

rough check (credit Archimedes)

area of circle around it = pi (3)^2 = 28.3 so or answer is not crazy

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