Question

what is the area of this figure? square kilometers

Explanation:

Step1: Calculate the area of the lower - left rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the lower - left rectangle with length \(l = 4\) km and width \(w = 4\) km, \(A_1=4\times4\).

$$A_1 = 16$$

Step2: Calculate the area of the upper - right rectangle

The upper - right rectangle has length \(l = 13\) km and width \(w = 4\) km. Using the area formula \(A = l\times w\), \(A_2 = 13\times4\).

$$A_2=52$$

Step3: Calculate the area of the middle rectangle (the part that connects the two rectangles)

The middle rectangle has length \(l=(8 - 4)\) km and width \(w=(13 - 9)\) km. First, \(8−4 = 4\) km and \(13−9 = 4\) km. Then, using the area formula \(A=l\times w\), \(A_3=(8 - 4)\times(13 - 9)\).

$$A_3=4\times4=16$$

Step4: Sum up the areas of the three rectangles

The total area \(A = A_1+A_2+A_3\). Substitute \(A_1 = 16\), \(A_2 = 52\), and \(A_3 = 16\) into the formula.

$$A=16 + 52+16$$

$$A=84$$

Answer:

84