Question

find the area of the shape. (sides meet at right angles.)

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 \(l = 3 + 1+2=6\)m and width \(w = 2\)m. So the area \(A_1=6\times2 = 12\) \(m^{2}\).

Step2: Calculate the area of the right rectangle

For the right rectangle, length \(l = 2\)m and width \(w = 4 - 2=2\)m. The area \(A_2=(3 + 1+2)\times2-(3\times2)= (6\times2)-(6)=6\) \(m^{2}\). The total area \(A=A_1 + A_2\). Another way:
We can also divide the figure into three rectangles.
First rectangle (left - most): area \(A_{a}=2\times(3 + 1+2)=12\) \(m^{2}\) (using \(A = l\times w\), \(l=(3 + 1+2)\), \(w = 2\)).
Second rectangle (upper middle): area \(A_{b}=1\times2=2\) \(m^{2}\) (using \(A = l\times w\), \(l = 2\), \(w = 1\)).
Third rectangle (lower middle): area \(A_{c}=1\times2=2\) \(m^{2}\) (using \(A = l\times w\), \(l = 2\), \(w = 1\)).
Fourth rectangle (right - most): area \(A_{d}=2\times4 = 8\) \(m^{2}\) (using \(A = l\times w\), \(l = 4\), \(w = 2\)).
Total area \(A=(3\times2)+(1\times2)+(1\times2)+(2\times4)=6 + 2+2 + 8=18\) \(m^{2}\).

Answer:

\(18\)