Lesson 15 β€” Activity 1: Estimating and Calculating the Area of Rectangles

Getting Ready

Area is a measure of how much space there is inside a shape. It is the number of square units required to cover a 2-D object.

You could calculate the area of walls in your home to determine how much paint you will need to buy.

Calculating the area of a shape or surface can be useful in everyday life. For example, you may need to know how much paint to buy to cover a wall or how much carpet to buy to cover a floor in your home.

Think about This:

Can you think of other instances when you might need to know the area of something?

Estimating the Area of Rectangles

A rectangle is a four-sided shape that has two sets of two sides that are equal in length. The longer sides are called the length while the shorter sides are called the width. All four corners are right angles. Right angles are usually shown by having a square drawn in the corner where the right angle is.

This image shows a rectangle.

The area of a rectangle can be estimated using a variety of methods. One method is to use grid paper. Count the number of squares inside the shape. Each square is one unit.

This image shows how to estimate area.

Area = 6 x 3 = 18 square units

Prove it! Use a geoboard and construct a rectangle that is three squares wide and six squares long. How many squares are there inside the rectangle?

You can use a geoboard from your classroom or use the virtual geoboard by clicking here.

(To use the virtual geoboard, choose the rectangle board for this activity. You will find it by clicking on the rectangle at the bottom of the page: Click on the green rectangle for the rectangular geoboard..)

To begin, select any colour of elastic and drag it up onto the board by holding down the left mouse key. When you are where you want to place the elastic, release your left mouse key. Move your mouse around and notice the elastic stretches as your mouse moves.


Try This:

Estimate the area of the following shape. You can prove your answer by using the geoboard once again.

Shape 1

7 x 5 = 35 square units

Calculating the Area of Rectangles

Formulas are equations used to make specific calculations. To calculate the area of a rectangle, you would use this formula:

A = l x w

Area is always an amount β€œsquared,” which is shown by writing the number 2 after and a little above the units.

For example, let's say you have a rectangle with a length of 4 mm and a width of 2 mm and you want to know what the area is, you could calculate it this way:

Use this shape to calculate area.

A = l x w                            

A = 4 x 2

A = 8 mm2

Notice that the answer contains mm2. This is because any time you calculate the area of something, the answer must contain the unit it was measured in so that anybody looking at your work knows just how big of an area you have calculated.

If you didn't put in the unit, the answer could just as easily have been 8 km2 or 8 m2.

Try This:

What if you had a rectangle that was 90 cm long and 27 cm wide? What would its area be? Use the formula above and put the unit in your answer. (You may use a calculator to solve.)

A = l x w
A = 90 x 27
A = 2,430 mm2

Images courtesy of www.imagesgoogle.com and K&E Studio. 

Go to the next page to try a Self-check Activity to further practise finding the area of rectangles.