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 $100$ meters.

1. Label all sides.

   Answer (a):

   

2. Find y in terms of $x$.

   Answer (b):

   $2y + 3x = 100$
   $2y = 100 − 3x$

   $y=\frac{100-3x}{2}$

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

   Hint (c):

   $\text{Area}_{\text{total}} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}}$

   More help (c):

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

   Use the Pythagorean Theorem to find the height. The area will be $\frac{(\text{height})(\text{base})}{2}$.