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Math Help - [SOLVED] geometry shapes

  1. #1
    britt12790
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    [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?
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  2. #2
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    Quote 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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