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geometry

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The shortest side of a polygon of area 196 sq. in. is 4 in. long. Find the area of a similar polygon whose shortest side is 8 in. long.

  • geometry -

    For similar shapes, the area ratio is proportional to the square of the length ratio for any corresponding sides.

    Area(#2)/Area(#1)
    = [(short side length#2/short side length#1)]^2 = (8/4)^2 = 4

    Thus the larger polygon (#2) has four times that of the smaller polygon #1), or
    A2 = 196 * 4 = 784 sq. in.

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