Lesson 15 — Activity 1: Area of a Rectangle



Getting Ready


Area is the number of square units required to cover a 2-D object. It is the space inside a flat, two-dimensional shape. For example, a carpet covers an area of the floor.

            

Courtesy of Pixabay

         

Think about This:


People calculate area for many purposes, such as covering floors with carpet, purchasing seed for fields, and buying paint for walls. 

    

    

Courtesy of Pixabay


Can you think of other examples of calculating area in your everyday life?      



Finding Area

Area can be determined using grids or geoboards and is calculated using equations called formulas.


Let's look at a grid example first.

 

Courtesy of ADLC

 

Count the number of squares inside the shape. Each square is one unit.

Area = 6 x 3 = 18 square units


Let's try finding area using a geoboard.

(You may use a geoboard in your classroom or click here to use a virtual geoboard.)

Construct a rectangle that is 3 squares wide and 6
squares long. How many squares are there inside the rectangle?

Courtesy of mathlearningcenter.org/geoboard

Area = 3 x 6 = 18 square units





Try This:

1. Determine the area of the shape on the grid below.

Courtesy of ADLC

Area =  7 x 5 = 35 square units


2. Use a geoboard to make a shape with this area: 8 x 5 = 40 square units.

(You may use a geoboard in your classroom or click here to use a virtual geoboard.


Your shape may look like this:



Courtesy of mathgeocenter.org/geoboard


Formulas are equations used to make specific calculations. The basic formula for calculating the area of rectangles is length times width (l × w). Area is always an amount “squared,” which is shown by writing the number 2 after and a little above the units.

Area = l x w

l x w = units2

OR

Area = h x w (h is height)

h x w = units2




As noted above, there are many instances of using area in our everyday lives. Look at this example:

Let's say you have a job installing carpets in homes. You will need to measure the length and width of a room to find the amount of carpet you must install.



Courtesy of Pixabay


The first room you are working in is the master bedroom. The length of the room is 3 metres and the width of the room is 9 metres.


You can use the formula for rectangles above to find the area:


A = l x w


A = 3 m x 9 m


A = 27 m2



Sometimes you may be given the area and the measurement of one side and asked to find the measurement of the other side. To do this you have to use algebra.

Let's say you have a rectangle that is 60 m2 in area and are told that one side is 6 m in length. How can you figure out the measurement of the other side, the width? Remember, you have to get the variable, in this case, w, by itself on one side of the equation:


A = l x w


60      6w
  6    =   6


10  =   w

The measurement of the unknown side is 10 m.




  Self-check!

Try this!

Try this activity to practice working with area of rectangles.


A rectangle has an area of  24 km2. One side of the rectangle is 12 km long. Find the missing side length.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mi mathcolor=¨#FFFFFF¨»A«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mi mathcolor=¨#FFFFFF¨»l«/mi»«mi mathcolor=¨#FFFFFF¨»w«/mi»«mspace linebreak=¨newline¨»«/mspace»«mn mathcolor=¨#FFFFFF¨»24«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»12«/mn»«mi mathcolor=¨#FFFFFF¨»w«/mi»«mspace linebreak=¨newline¨»«/mspace»«mfrac mathcolor=¨#62D3B3¨»«mn mathcolor=¨#FFFFFF¨»24«/mn»«mn»12«/mn»«/mfrac»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mfrac mathcolor=¨#62D3B3¨»«mrow»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mn»12«/mn»«/menclose»«mi mathcolor=¨#FFFFFF¨»w«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn»12«/mn»«/menclose»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mn mathcolor=¨#FFFFFF¨»2«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mi mathcolor=¨#FFFFFF¨»k«/mi»«mi mathcolor=¨#FFFFFF¨»m«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mi mathcolor=¨#FFFFFF¨»w«/mi»«/mstyle»«/math»

The missing side  of this rectangle is 2 km long.


Find the area of a rectangle if it is 17 cm long and 4 cm wide.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»A«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mi mathcolor=¨#FFFFFF¨»l«/mi»«mi mathcolor=¨#FFFFFF¨»w«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi mathcolor=¨#FFFFFF¨»A«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»(«/mo»«mn mathcolor=¨#FFFFFF¨»17«/mn»«mo mathcolor=¨#FFFFFF¨»)«/mo»«mo mathcolor=¨#FFFFFF¨»(«/mo»«mn mathcolor=¨#FFFFFF¨»4«/mn»«mo mathcolor=¨#FFFFFF¨»)«/mo»«mspace linebreak=¨newline¨»«/mspace»«mi mathcolor=¨#FFFFFF¨»A«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»68«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mi mathcolor=¨#FFFFFF¨»c«/mi»«msup»«mi mathcolor=¨#FFFFFF¨»m«/mi»«mn mathcolor=¨#FFFFFF¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»

The area of this rectangle is 68 cm2. (Remember, area is expressed in units squared.)




Digging Deeper

 

Click here to try a game to find area. (Choose the section on area.)