i need to find the area of a octagon with a perimeter of 40 ft and also find the same thing for a triangle and trapezoid. can you please help me fast?

Printable View

- Feb 14th 2006, 12:02 PMbritt12790[SOLVED] geometry shapes
i need to find the area of a octagon with a perimeter of 40 ft and also find the same thing for a triangle and trapezoid. can you please help me fast?

- Feb 14th 2006, 02:38 PMThePerfectHackerQuote:

Originally Posted by**britt12790**

$\displaystyle A=\frac{1}{2}s\sin\frac{180}{n}$

Where $\displaystyle n$ is the number of sides and,

$\displaystyle s$ is the length of the sides.

But since it perimeter is 40 and there are 8 sides then each sides is 5. Thus,

$\displaystyle A=\frac{1}{2}(5)\sin\frac{45}{2}$

But $\displaystyle \sin\frac{45}{2}=\frac{\sqrt{2-\sqrt{2}}}{2}$.

Thus,

$\displaystyle A=\frac{5}{4}\sqrt{2-\sqrt{2}}$