Question

A park has the shape of a trapezoid.

Answer 1

Answer:

$the\: answer \: is \: {108 \: mi.}^{2}$

Step-by-step explanation:

Given hints:

a.) A park has the shape of a trapezoid.

b.) The shortest side of the park and its height have the same dimension.

In the given figure, the shortest side of the park is A. Since it is mentioned that the height and its shortest side have the same dimension, we can therefore say that the measure of A is 9 mi.

The longest side appears to be 6 miles longer that the shortest side:

$b = a + 3 \: mi + 3 \: mi = a + 6 \: mi$

Therefore, B = A + 6 mi. = 9 mi. + 6 mi. = 15 mi.

Let's now determine the area of the park:

$area = \frac{a + b}{2} h$

Where,

A = 9 mi.

B = 15 mi

H = 9 mi.

$area = \frac{a + b}{2} h \\ \\ = \frac{9 \: mi. +15 \: mi. }{2} (9 \: mi.) \\ \\ = \frac{24 \: mi.}{2}(9 \: mi.) \\ \\ = (12 \: mi.)(9 \: mi. \\ \\ area = {108 \: mi.}^{2}$

The area of the park is 108 mi^2.