Question

area: perimeter: 2. calculate the area of the shaded region. a) area:

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 \(7\) and the width is \(6\). So, \(A_{large}=7\times6 = 42\).

Step2: Calculate the area of the un - shaded part

The un - shaded part can be considered as two rectangles. One rectangle has dimensions \((2 + 3)\times1\) and the other has dimensions \((2 + 3)\times1\) (by observing the lengths). The total length of the un - shaded part (in one dimension) is \(2+3=5\). The combined height of the two un - shaded sub - rectangles is \(1 + 1=2\). So the area of the un - shaded part \(A_{un - shaded}=(2 + 3)\times(1 + 1)=5\times2 = 10\) (alternatively, we can think of it as two rectangles: one with area \((2 + 3)\times1=5\) and another with area \((2 + 3)\times1 = 5\), so \(A_{un - shaded}=5+5 = 10\))

Step3: Calculate the area of the shaded part

The area of the shaded part \(A_{shaded}=A_{large}-A_{un - shaded}\). Substitute \(A_{large}=42\) and \(A_{un - shaded}=10\) into the formula. So \(A_{shaded}=42- 10=32\)

Answer:

\(32\)