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?

   Hint (a):

   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.

   More Help (a):

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

   

   Step (a):

   $\text{tan}(78^\circ)=\frac{8}{x}$

   Answer (a):

   $≈ 74.24$ meters²

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

   Answer (b):

   $≈ 36.2$ meters

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

   Hint (c):

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