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A farmer with an eye for the unusual has decided to build a pentagonal enclosure whose shape will be a rectangle with an equilateral triangle sitting on top of it. (See figure at right.) The perimeter is meters.

  1. Label all sides.

    Same pentagon, labels added to sides, right vertical is y, right & left slanted are each x.

  2. Find y in terms of .

  3. Find the area of the figure as a function of .

    To find the area of the triangle, drop an altitude forming two congruent triangles. The diagonal will be ''.

    Use the Pythagorean Theorem to find the height. The area will be .

Pentagon, bottom side horizontal, labeled, x, with 2 vertical sides, left labeled, y, & 2 slanted sides