Question

1. for each figure below.

• write a multiplication expression to represent the area of the shaded region.
• find the area of the shaded region, in square units, using any strategy.

a)

Explanation:

Step1: Determine the dimensions of the whole rectangle

The whole rectangle has length \(6\) (since each small segment is \(1\) unit and there are \(6\) segments along the length) and width \(3\) ( \(3\) segments along the width). So the area of the whole rectangle is \(A = 6\times3=18\) square units.

Step2: Count the number of shaded parts

There are \(13\) shaded small - rectangles (each of area \(1\times1 = 1\) square unit). But we can also use a fraction approach. The length of the shaded part: if we consider the length as divided into \(6\) equal parts, the shaded length is \(\frac{5}{6}\) of the total length. The width is divided into \(3\) equal parts (all shaded). The area of a rectangle is \(A=l\times w\). The multiplication expression for the area of the shaded region is \(3\times\frac{5}{6}\)

Step3: Calculate the area using the multiplication expression

$$3\times\frac{5}{6}=\frac{3\times5}{6}=\frac{15}{6}=\frac{5}{2} = 2.5$$

Answer:

The multiplication expression is \(3\times\frac{5}{6}\), and the area of the shaded region is \(2.5\) square units.