Thread:

1. [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?

2. Originally Posted by britt12790
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?
Assuming it is a regular octagon meaning that angles and sides are equal then using the formula,
$A=\frac{1}{2}s\sin\frac{180}{n}$
Where $n$ is the number of sides and,
$s$ is the length of the sides.

But since it perimeter is 40 and there are 8 sides then each sides is 5. Thus,
$A=\frac{1}{2}(5)\sin\frac{45}{2}$
But $\sin\frac{45}{2}=\frac{\sqrt{2-\sqrt{2}}}{2}$.
Thus,
$A=\frac{5}{4}\sqrt{2-\sqrt{2}}$
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