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Math Help - Help on fencing required

  1. #1
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    Help on fencing required

    Problem here and I have it drawn out, and made my right angle, but kinda stuck.

    Building is shaped like a pentagon with a 92.5 m on each side. A fence surrounds the building to form a circle, and each corner of the building is to be 25.0 m from the closest point on the fence. How much fencing is required.

    I know I cut the length to 46.25 m and I have the 90 degree angle, I am not sure what to do next.
    Any ideals. thanks
    Joanne
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  2. #2
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    Quote Originally Posted by bradycat View Post
    Problem here and I have it drawn out, and made my right angle, but kinda stuck.

    Building is shaped like a pentagon with a 92.5 m on each side. A fence surrounds the building to form a circle, and each corner of the building is to be 25.0 m from the closest point on the fence. How much fencing is required.

    I know I cut the length to 46.25 m and I have the 90 degree angle, I am not sure what to do next.
    Any ideals. thanks
    Joanne
    Let the radius of the fencing circle = R.
    Let the radius of the circle circumscribing the pentagon = r

    Then: R = r + 25.
    So you have to find r. Any interior angle of the pentaon = 540/5=108.

    Join center of pentagon (O) with 2 arbitrary vertices of the pentagon (let's say A and B)
    Take aside triangle AOB, with OA=OB=r, angle A = angle B = 54 and side AB=92.5

    Now drop the altitude from O, which will bisect AB at M.

    Triangle OAM is right angled, with angle M = 90 degrees, angle A = 54 degrees, side AM = 92.5/4=46.25 and you can find the side OA (that is r) by using trigonometric ratios.

    Once you have found r, you know R, and once you know R you can calculate the circumference of the fencing circle = 2*\Pi*R
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