Question

four figures are shown. each represents one whole. which figure is shaded to represent $\frac{1}{3}$ of the area of the whole? a. figure y b. figure w c. figure z d. figure x

Explanation:

Step1: Calculate the fraction of shaded part for each figure

• Figure W:

The circle is divided into 3 equal - sized sectors. The number of shaded sectors is 1. So the fraction of the shaded part is \(\frac{1}{3}\).

• Figure X:

The square is divided into 4 equal - sized smaller squares. The number of shaded smaller squares is 1. So the fraction of the shaded part is \(\frac{1}{4}\).

• Figure Y:

Let the length of the rectangle be \(l\) and the width be \(w\). The area of the rectangle \(A = l\times w\). The area of the triangle (shaded part) \(A_{triangle}=\frac{1}{2}\times l\times w\). So the fraction of the shaded part is \(\frac{1}{2}\).

• Figure Z:

The rectangle is divided into 3 equal - sized smaller rectangles. The number of shaded smaller rectangles is 2. So the fraction of the shaded part is \(\frac{2}{3}\).

Answer:

B. Figure W