Question

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a rectangular region is removed from another rectangular region to create the shaded regions shown below. find the combined area of the shaded regions.
8 m
4 m
16 m
72 m²

Explanation:

Step1: Calculate the area of the large rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the large rectangle, \(length = 16\space m\) and \(width=8\space m\). So, \(A_{large}=16\times8 = 128\space m^{2}\).

Step2: Calculate the area of the removed rectangle

The removed rectangle has \(width = 8\space m\) and \(length = 4\space m\). Using the area formula \(A = length\times width\), \(A_{removed}=4\times8=32\space m^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A_{shaded}=A_{large}-A_{removed}\). Substitute the values: \(A_{shaded}=128 - 32=96\space m^{2}\).

Answer:

\(96\space m^{2}\)