Question

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

Explanation:

Step1: Divide the polygon into three rectangles

Let's divide the given polygon into three non - overlapping rectangles.

Step2: Calculate the area of each rectangle

• First rectangle (left - most):

The dimensions are \(2\times1\) (height \( = 1\) cm, width \(=2\) cm). Using the formula for the area of a rectangle \(A = l\times w\), the area \(A_1=2\times1 = 2\space cm^{2}\).

• Second rectangle (middle):

The width is \(2 + 3+3-(2 + 3)=3\) cm and the height is \(1 + 2=3\) cm. Using the formula \(A = l\times w\), the area \(A_2 = 3\times1=3\space cm^{2}\).

• Third rectangle (right - most):

The dimensions are \(3\times4\) (length \(l = 3\) cm, width \(w = 4\) cm). Using the formula for the area of a rectangle \(A=l\times w\), the area \(A_3=3\times4=12\space cm^{2}\).

Step3: Sum up the areas of the rectangles

The total area \(A=A_1 + A_2+A_3\). Substitute \(A_1 = 2\), \(A_2 = 3\) and \(A_3=12\) into the formula.
\(A=2 + 3+12\)

Answer:

\(17\)