- Perimeter and Area of Polygons
- Home
- Sides of polygons having the same perimeter
- Finding the missing length in a figure
- Perimeter of a piecewise rectangular figure
- Area of a rectangle involving fractions
- Distinguishing between the area and perimeter of a rectangle
- Areas of rectangles with the same perimeter
- Word problem involving the area of a square or a rectangle
- Finding the side length of a rectangle given its perimeter or area
- Area of a piecewise rectangular figure
- Area between two rectangles
- Finding the area of a right triangle on a grid
- Finding the area of a right triangle or its corresponding rectangle
- Area of a triangle
- Finding the area of a trapezoid on a grid by using triangles and rectangles
- Area involving rectangles and triangles
- Area of a parallelogram
- Area of a trapezoid
- Finding the perimeter or area of a rectangle in the coordinate plane

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# 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