Home > AC > Chapter 16 > Lesson 16.9.2.2 > Problem9-87

9-87.

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.

2. Find y in terms of $x$.

$2y + 3x = 100$
$2y = 100 − 3x$

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

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

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

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 $\frac{(\text{height})(\text{base})}{2}$.