Question

1 unit
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 small tile side length

The big square has side length 1 unit, divided into 7 columns and 8 rows. So each small tile's side length is $\frac{1}{7}$ units (horizontal) and $\frac{1}{8}$ units (vertical).

Step2: Calculate small tile area

Area of a rectangle is length × width.
$\text{Area} = \frac{1}{7} \times \frac{1}{8} = \frac{1}{56}$

Step3: Count shaded tiles

The shaded rectangle has 6 columns and 5 rows, so total shaded tiles: $6 \times 5 = 30$

Step4: Calculate shaded rectangle area

Multiply number of shaded tiles by area of one tile.
$\text{Area} = 30 \times \frac{1}{56} = \frac{30}{56} = \frac{15}{28}$

Answer:

1. Each small tile has side lengths $\frac{1}{7}$ units and $\frac{1}{8}$ units.
2. The area of each small tile is $\frac{1}{56}$ square units.
3. The area of the shaded rectangle is $\frac{15}{28}$ square units.