Question

find the area of this rectangle by using the tiling method. first determine the length and width of the rectangle by representing the shaded region of the tile with a fraction. then determine the area of the rectangle using those fractions. (note: the rectangle is not to scale.)

Explanation:

Step1: Determine length fraction

The length - related tile has 4 equal parts and 2 are shaded. So the length fraction $l=\frac{2}{4}=\frac{1}{2}$.

Step2: Determine width fraction

The width - related tile has 4 equal parts and 3 are shaded. So the width fraction $w = \frac{3}{4}$.

Step3: Calculate area

The area of a rectangle is $A=l\times w$. Substitute $l=\frac{1}{2}$ and $w=\frac{3}{4}$ into the formula: $A=\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}$.

Answer:

$\frac{3}{8}$