Question

find the area of the polygon.
type your answer in the box.
the area is 17 cm².

Explanation:

Step1: Divide the polygon into rectangles

We can divide the given polygon into three rectangles.

Step2: Calculate the area of each rectangle

• For the first rectangle (left - most): The dimensions are \(2\times2\). Using the formula for the area of a rectangle \(A = l\times w\), we have \(A_1=2\times2 = 4\space cm^{2}\).
• For the second rectangle (middle): The length is \(3\) and the width is \(1 + 4=5\). So \(A_2 = 3\times1=3\space cm^{2}\).
• For the third rectangle (right - most): The dimensions are \(3\times4\). Using the formula \(A = l\times w\), we get \(A_3=3\times4 = 12\space cm^{2}\).

Step3: Sum up the areas of the rectangles

The total area \(A=A_1 + A_2+A_3\). Substitute the values: \(A=4 + 3+12\).

Answer:

\(17\space cm^{2}\)