Question

find the area of the shaded region. explain or show your reasoning. use \square units\ in your answer.
1.
8
1/2
8×1/2 or

Explanation:

Step1: Recall the formula for the area of a rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.

Step2: Identify the length and width of the shaded region

The length of the shaded - region (same as the whole rectangle) \(l = 8\), and the width of the shaded region \(w=\frac{1}{2}\) (since the height of the whole rectangle is \(\frac{1}{2}\) and the shaded part is half of the height of each small rectangle, but actually, if we consider the whole figure as a rectangle with length \(l = 8\) and width \(w=\frac{1}{2}\), we can directly use the formula).

Step3: Calculate the area

Substitute \(l = 8\) and \(w=\frac{1}{2}\) into the formula \(A=l\times w\). So \(A = 8\times\frac{1}{2}\). Using the rule of multiplying a whole number by a fraction (\(a\times\frac{b}{c}=\frac{a\times b}{c}\)), we have \(A=\frac{8\times1}{2}\). Since \(8\div2 = 4\), \(A = 4\).

Answer:

4 square units