Area of a rectangle involving fractions

Area − The amount of surface a figure covers is its area.

For example, the perimeter measures the length of a fence going around a garden. Area measures the entire floor space that is going to be covered with a carpet.

A fraction is a number that is greater than zero but less than 1.

When two fractions that are both less than 1 are multiplied together, their product is smaller than either fraction.

In this lesson, we find areas of rectagular figures that have fractional lengths and widths.

Formula for the area of a rectangle involving fractions

If a rectangular figure has length and width of $\frac{a}{b}$ and $\frac{c}{d}$ where a, b, c and d are whole numbers, then the area of the rectangular figure is given by

Area = l × w = $ \mathbf{\frac{a}{b}}$ × $\mathbf{\frac{c}{d}}$ = $\mathbf{\frac{ab}{cd}}$ square units

A lake is $\frac{2}{5}$ mile in length and $\frac{3}{7}$ mile in width. What is the area of the lake?

Solution

Step 1:

Area of rectangle = l × w square units; l = length; w = width

Step 2:

Area of the lake = l × w = $\frac{2}{5}$ × $\frac{3}{7}$ = $\frac{6}{35}$ square mile

An island in the Pacific Ocean was $\frac{8}{13}$ miles wide and $\frac{9}{11}$ miles long. What is the area of the island?

Solution

Step 1:

Area of rectangle = l × w square units; l = length; w = width

Step 2:

Area of the island = l × w = $\frac{8}{13}$ × $\frac{9}{11}$ = $\frac{72}{143}$ square miles