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Math Help - Area problem

  1. #1
    Junior Member
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    Dec 2009
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    Area problem

    Melissa has moved to Australia to become an emu rancher. She has acquired a square plot of land 1 km by 1 km, with an emu house located at the center of the southern edge. The emus are outted with special tracking devices that must remain no more than 1 km from the emu
    house, so the northern border of the ranch has a fence which is part of a circle. Calculate the area within the fence. (See pic below.)
    Attached Thumbnails Attached Thumbnails Area problem-emu.bmp  
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    Assuming the emu house is a point (call it A), and the circular boundary intersects the plot of land at points B and C, then ABC is an equilateral triangle. The area enclosed by AB, AC, and the circular boundary is therefore 1/6 the area of a circle with radius 1. Now you just add to this the area of the rest of the plot of land, which is two right triangles with a hypotenuse of 1 and an interior angle of 60 degrees.
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