Question

what is the area of this figure?
4 km
3 km
5 km
4 km
7 km
5 km
7 km
15 km
square kilometers

Explanation:

Step1: Calculate the area of the left rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the left rectangle, length \(l = 7\) km and width \(w = 5\) km. So, \(A_1=7\times5 = 35\) \(km^{2}\)

Step2: Calculate the area of the middle rectangle

The height of the middle rectangle is \(3 + 5=8\) km (since the total height of the figure can be related to the left - rectangle's height and the given segment). Its width is \(4\) km. Using the area formula \(A = length\times width\), \(A_2 = 4\times8=32\) \(km^{2}\)

Step3: Calculate the area of the right rectangle

For the right rectangle, length \(l=(15-(7 + 4))=4\) km and width \(w = 7\) km. Using the area formula \(A = length\times width\), \(A_3=4\times7 = 28\) \(km^{2}\)

Step4: Sum up the areas

The total area \(A=A_1 + A_2+A_3\). Substitute \(A_1 = 35\), \(A_2=32\), and \(A_3 = 28\) into the formula: \(A=35 + 32+28=95\) \(km^{2}\)

Answer:

\(95\)