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

Answer

Explanation:

Step1: Divide the figure into rectangles and a triangle

We can divide the figure into two rectangles and a right - triangle.

Step2: Calculate the area of the first rectangle

The first rectangle has length $l_1 = 7$ mi and width $w_1=2$ mi. The area formula for a rectangle is $A = l\times w$. So, $A_1=l_1\times w_1=7\times2 = 14$ square miles.

Step3: Calculate the area of the second rectangle

The second rectangle has length $l_2=6$ mi and width $w_2 = 4$ mi. So, $A_2=l_2\times w_2=6\times4 = 24$ square miles.

Step4: Calculate the base and height of the triangle

The base of the triangle $b=(2 + 6+2)-2=8$ mi and the height of the triangle $h = 6$ mi.

Step5: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}\times b\times h$. So, $A_3=\frac{1}{2}\times8\times6=24$ square miles.

Step6: Calculate the total area of the figure

The total area $A = A_1+A_2+A_3$. So, $A=14 + 24+24=62$ square miles.