Question

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

a.

Explanation:

Step1: Determine the formula for the area of a rectangle

The area of a rectangle is \(A = length\times width\). The large rectangle has length \(l = 5\) and width \(w=2\), so its area \(A_{total}=5\times2 = 10\).

Step2: Find the fraction of the shaded region

The shaded region has length \(5\) and width \(1\). The fraction of the shaded region with respect to the whole rectangle is \(\frac{1}{2}\) (since the width of the shaded part is \(1\) and the total width is \(2\)).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A_{shaded}\) can be written as an expression \(A_{shaded}=5\times1\) (using the formula \(A = l\times w\) for the shaded rectangle). Another way is \(A_{shaded}=\frac{1}{2}\times(5\times 2)\).

$$A_{shaded}=5\times1=5$$

Answer:

The expression for the area of the shaded region is \(5\times1\) (or \(\frac{1}{2}\times(5\times2)\)) and the area is \(5\).