Question

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

Explanation:

Step1: Divide the figure into rectangles and a trapezoid

We can divide the given figure into two rectangles and a trapezoid.

Step2: Calculate the area of the first rectangle

The first rectangle has length \(l_1 = 8\) mi and width \(w_1=3\) mi. The area formula for a rectangle is \(A = l\times w\). So \(A_1=8\times3 = 24\) square - miles.

Step3: Calculate the area of the second rectangle

The second rectangle has length \(l_2 = 3\) mi and width \(w_2 = 2\) mi. So \(A_2=3\times2=6\) square - miles.

Step4: Calculate the area of the trapezoid

The trapezoid has bases \(b_1 = 8\) mi and \(b_2 = 6\) mi and height \(h=(2 + 3)=5\) mi. The area formula for a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\). So \(A_3=\frac{(8 + 6)\times5}{2}=\frac{14\times5}{2}=35\) square - miles.

Step5: Calculate the total area of the figure

The total area \(A = A_1+A_2+A_3\). So \(A=24 + 6+35=65\) square - miles.

Answer:

65