Posted by **Geomtery** on Tuesday, February 21, 2012 at 10:11pm.

Please Help Me!

Find the area of this polygon rround to the nearest tenth.

The polygon is a hexagon with six sides, and all they give is the apothem which is 6 inches long, what is the area?

I know the formula is A=1/2ap

But can anyone help!

- Geometry -
**Steve**, Wednesday, February 22, 2012 at 10:44am
The polygon can be divided up into six triangles, each with base=s and height=6

Since it is a hexagon, you know the triangles are equilateral triangles, with height (apothem) = s*sqrt(3)/2

So, if the apothem is 6, 6 = s*sqrt(3)/2, and s = 12/sqrt(3) = 4sqrt(3)

A = 1/2 * a * p

= 1/2 * 6 * 6*4sqrt(3)

= 72sqrt(3)

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