Question

this model shows a unit square divided into smaller same - size tiles. the shaded tiles form a rectangle.
use fractions to complete the sentences.
each small tile has side lengths □ units and units.
the area of each small tile is square units.
the area of the shaded rectangle is square units.

Explanation:

Step1: Find side - length of small tile

The unit square has side - length \(1\) unit. The square is divided into \(6\) equal parts along one side and \(5\) equal parts along the other side.
The side - length of each small tile:
If we divide a side of length \(1\) unit into \(6\) equal parts (horizontal side), the length of each part is \(\frac{1}{6}\) unit. If we divide a side of length \(1\) unit into \(5\) equal parts (vertical side), the length of each part is \(\frac{1}{5}\) unit.

Step2: Calculate area of small tile

The area of a rectangle (small tile) is \(A = l\times w\). Using \(l=\frac{1}{6}\) and \(w = \frac{1}{5}\), we get \(A=\frac{1}{6}\times\frac{1}{5}=\frac{1}{30}\) square units.

Step3: Calculate area of shaded rectangle

Count the number of small tiles in the shaded rectangle. There are \(4\times4 = 16\) small tiles.
The area of the shaded rectangle is \(16\times\frac{1}{30}=\frac{16}{30}=\frac{8}{15}\) square units.

Answer:

Each small tile has side lengths \(\frac{1}{6}\) units and \(\frac{1}{5}\) units. The area of each small tile is \(\frac{1}{30}\) square units. The area of the shaded rectangle is \(\frac{8}{15}\) square units.