Question

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

Explanation:

Step1: Calculate the area of the large rectangle

The formula for the area of a rectangle is \(A = length\times width\). The length of the large rectangle is \(15\) m and the width is \(7\) m. So the area \(A_{1}=15\times7 = 105\) \(m^{2}\).

Step2: Calculate the area of the small rectangle (the "cut - out" part)

The length of the small rectangle is \(5\) m and the width is \(4\) m. Using the area formula \(A = length\times width\), we get \(A_{2}=5\times4=20\) \(m^{2}\).

Step3: Calculate the area of the figure

The area of the figure \(A\) is the area of the large rectangle minus the area of the small rectangle. So \(A = A_{1}-A_{2}\). Substitute \(A_{1}=105\) \(m^{2}\) and \(A_{2} = 20\) \(m^{2}\) into the formula: \(A=105 - 20=85\) \(m^{2}\).

Answer:

\(85\) \(m^{2}\)