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.

## Answer this Question

## Related Questions

- geometry - How do you find the perimeter of a regular dodecagon whose side is ...
- Algebra - What is the measure of each of the interior angles of these regular ...
- geometry - 1. the sum of the interior angle measures of a convex dodecagon. 2. ...
- maths - a regular dodecagon has a side lenght of 5.6cm find the side lenght of a...
- Algebra I - Rectangle ABCD has vertices C and d on the x-axis and vertices A and...
- Math - Check my answer please? Yuri is wrapping presents. The first box measures...
- Calculus-Steve - Find the area of the region between the graphs of f(x)=3x+8 and...
- Calculus - Center of Mass - Find the exact coordinates of the centroid given the...
- calculus(Lab) - Well, first graph the graph of f(x)=-1/10x^2 + 3 2. We are going...
- math - i have a question in math (( distance between two points )) the vertices ...

More Related Questions