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Geometry

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Find the area of a regular pentagon with radius 3cm. Round to the nearest tenth.

No picture is given, but I believe a circle can surround the figure. I'm not really sure how to find the area of the figure when the side length isn't given. Can you guys help me?

Thanks much!

  • Geometry - ,

    if it fits inside the circle, the distance from the center to a point of the pentagon is 3 cm.
    There are five isoceles triangles in the pentagon, each with an angle at the center of 360/5 = 72 degrees and sides of 3 cm
    What we have to do is find the area of that triangle and multiply by 5
    we need the base of the triangle and its altitude
    look at right triangle formed by altitude and base
    72/2 = 36 degrees
    hypotenuse = 3
    so altitude /3 = cos 36
    half base/3 = sin 36
    altitude = 2.43
    half base = 1.76
    area of isoceles triangle = half base * altitude = 4.28
    5 times triangle area = 21.4
    ===============================
    rough check (credit Archimedes)
    area of circle around it = pi (3)^2 = 28.3 so or answer is not crazy

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