Posted by **Knights** on Tuesday, December 18, 2012 at 10:35am.

The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon.

first, what is the area of a dodecagon and second how to find it with just the distance between two oppositve vertices.

i found that a dodecagon can be divided into 24 triangles: an apothem, half of one of the sides, and half of the distance between two oppositite vertices of the dodecagon. So how do we do this ?

BTW I did not learn trigonometry so this can be figured out through geometry.

Thanks a lot for helping me if you can.

- please help - area of a dodecagon? -
**Steve**, Tuesday, December 18, 2012 at 11:41am
the diagonal is the diameter of the circumscribed circle.

The area of a dodecagon inscribed in a circle of radius R is 3R^2.

So, here R=1, and A = 3

You can find a geometric derivation of the area in Euclid Book IV, but it's heavy going.

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