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 \(l = 3\)m and width \(w = 2\)m. So, \(A_1=3\times2 = 6\) \(m^{2}\).

Step2: Calculate the area of the middle rectangle

The height of the middle rectangle is \(4-(2) = 2\)m (by subtracting the height of the left - lower rectangle from the total height of the right - side rectangles). The length of the middle rectangle is \(1 + 3+1=5\)m. Using the area formula \(A = length\times width\), \(A_2 = 5\times2=10\) \(m^{2}\).

Step3: Calculate the area of the right rectangle

For the right rectangle, length \(l = 2\)m and width \(w = 4\)m. Using the area formula \(A = length\times width\), \(A_3=2\times4 = 8\) \(m^{2}\).

Step4: Sum up the areas

The total area \(A=A_1 + A_2+A_3\). Substitute \(A_1 = 6\), \(A_2 = 10\), and \(A_3 = 8\) into the formula: \(A=6 + 10+8=24\) \(m^{2}\).

Answer:

\(24\)