Question

what is the area of this figure? write your answer using decimals, if necessary. square miles

Explanation:

Step1: Calculate area of rectangle 1

The first rectangle has length $l_1 = 5$ mi and width $w_1=4$ mi. The area formula for a rectangle is $A = l\times w$. So, $A_1=5\times4 = 20$ square - miles.

Step2: Calculate area of rectangle 2

The second rectangle has length $l_2 = 2$ mi and width $w_2 = 6$ mi. Using the area formula for a rectangle $A = l\times w$, we get $A_2=2\times6 = 12$ square - miles.

Step3: Calculate area of trapezoid

The trapezoid has bases $b_1 = 7$ mi and $b_2=2$ mi and height $h = 6$ mi. The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. So, $A_3=\frac{(7 + 2)\times6}{2}=\frac{9\times6}{2}=27$ square - miles.

Step4: Calculate total area

The total area $A$ of the figure is the sum of the areas of the two rectangles and the trapezoid. $A=A_1+A_2+A_3$. Substituting the values we found: $A = 20+12 + 27=59$ square - miles.

Answer:

59