Question

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

Explanation:

Step1: Calculate the area of the triangle

The base of the triangle is \(11\) mi and the height is \(11 - 4=7\) mi. The area of a triangle is \(A=\frac{1}{2}\times base\times height\). So, \(A_1=\frac{1}{2}\times11\times7=\frac{77}{2} = 38.5\) square miles.

Step2: Calculate the area of the large rectangle

The length of the large rectangle is \(9\) mi and the width is \(4\) mi. The area of a rectangle is \(A = length\times width\). So, \(A_2=9\times4 = 36\) square miles.

Step3: Calculate the area of the small rectangle

The length of the small rectangle is \(4\) mi and the width is \(2\) mi. The area of a rectangle is \(A = length\times width\). So, \(A_3=4\times2=8\) square miles.

Step4: Sum up the areas

The total area \(A=A_1 + A_2+A_3\). Substitute the values: \(A = 38.5+36 + 8\).

Answer:

\(82.5\)