Question

1. for each diagram, write an expression for the area of the shaded region. then find the area.

a.
b.
c.

Explanation:

Step1: Find the area of the whole rectangle

The area of a rectangle is \(A = length\times width\). For each part, the length and width of the whole rectangle can be counted from the diagram.

• Part a:

The length of the whole rectangle is \(5\) (since there are \(5\) units of length \(1\)) and the width is \(2\) (since there are \(2\) units of width \(1\)). So the area of the whole rectangle \(A_{total}=5\times2 = 10\). The shaded part is half of the whole rectangle. The expression for the area of the shaded region is \(\frac{1}{2}\times(5\times2)\).

$$ \frac{1}{2}\times(5\times 2)=\frac{1}{2}\times10 = 5 $$

• Part b:

The length of the whole rectangle is \(3\) and the width is \(3\). So the area of the whole rectangle \(A_{total}=3\times3=9\). The shaded part is \(\frac{2}{3}\) of the whole rectangle. The expression for the area of the shaded region is \(\frac{2}{3}\times(3\times3)\).

$$ \frac{2}{3}\times(3\times3)=\frac{2}{3}\times9 = 6 $$

• Part c:

The length of the whole rectangle is \(4\) and the width is \(3\). So the area of the whole rectangle \(A_{total}=4\times3 = 12\). The shaded part is \(\frac{5}{6}\) of the whole rectangle. The expression for the area of the shaded region is \(\frac{5}{6}\times(4\times3)\).

$$ \frac{5}{6}\times(4\times3)=\frac{5}{6}\times12=10 $$

Answer:

a. The expression is \(\frac{1}{2}\times(5\times2)\), and the area is \(5\).
b. The expression is \(\frac{2}{3}\times(3\times3)\), and the area is \(6\).
c. The expression is \(\frac{5}{6}\times(4\times3)\), and the area is \(10\).