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7-62.

The Portland Zoo is building a new children’s petting zoo pen that will contain six goats. One of the designs being considered is shown at right (the shaded portion).

  1. What is the area of the petting zoo?

    Find the area of the pen by first finding the area of the trapezoid and then subtracting the area of the quarter circle. Notice the congruent segments on the right side.

    Draw a height to make a right triangle. Use trigonometry to find the unknown side lengths.

    A rectangle with a quarter circle removed from the upper left corner and a triangle appended to the right side. The radius of the circle is 4 meters. The rest of the top edge is 6 meters. The length of the remaining part of the left side is the same as the radius. For the triangle appended on the right side, there is a 78 degree angle opposite the right side of the rectangle.

    meters2

  2. How many meters of fence are needed to enclose the petting zoo area.

    meters

  3. Animal rights advocates call for each goat to have at least 1.1 square meters to frolic. Will this pen design meet animal rights advocates criteria? Explain.

    There are six goats. How much area does each goat have?

A rectangle with a quarter circle removed from the upper left corner and a triangle appended to the right side. The radius of the circle is 4 meters. The rest of the top edge is 6 meters. The length of the remaining part of the left side is the same as the radius. For the triangle appended on the right side, there is a 78 degree angle opposite the right side of the rectangle.