Question

what is the area of the polygon shown below?

Explanation:

Step1: Divide the polygon into a square and a triangle

The side - length of the square is \(5\) mm. The base of the triangle is \(5 + 8=13\) mm and the height is \(12\) mm.

Step2: Calculate the area of the square

The area formula of a square is \(A_{square}=s\times s\), where \(s = 5\) mm. So \(A_{square}=5\times5 = 25\) \(mm^{2}\).

Step3: Calculate the area of the triangle

The area formula of a triangle is \(A_{triangle}=\frac{1}{2}\times b\times h\), where \(b = 13\) mm and \(h = 12\) mm. So \(A_{triangle}=\frac{1}{2}\times13\times12=78\) \(mm^{2}\).

Step4: Calculate the total area of the polygon

The total area \(A = A_{square}+A_{triangle}\). So \(A=25 + 78=103\) \(mm^{2}\).

Answer:

\(103\) \(mm^{2}\)