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Problems with Areas


Now that we know how to calculate the area of rectangles, we can use it  to work out actual problems we may have. That can include working out the length or width, if we know the area of our rectangle. Imagine if you wanted to:

  • cover your desk with plastic, to protect it,
  • paint the top of your desk, to change the colour, or 
  • put a rug down on the floor of your bedroom or playroom.

Let's see how we might do this, in the video.


Different units of measurement

It doesn't matter what units of measurement we use, but we should make sure our answer is expressed in the same unit of measurement, squared. So, if our length and width are in millimetres (mm), the area will be mm2.

In this applet, you can:

  • change the width and length,
  • choose mm, cm or m as the unit of measurement to see the area's unit of measurement, and 
  • change the colour!


Practice questions

Question 1

A rectangular driveway is $8$8 m long and $3$3 m wide.

  1. What is the area of the driveway?

Question 2

Katrina is digging a rectangular garden bed to plant some new hedging.

  1. If the garden bed is $0.5$0.5 m wide and $8$8 m long, what is the total area of the garden bed?

  2. Each hedge plant fills an area that is the same as $1$1 square metre. How many hedge plants are needed to fill Katrina’s garden bed?

Question 3

A kitchen floor is tiled with the tiles shown in the picture. If $30$30 tiles are needed to tile the floor, what is the total area of the floor? Give your answer in square centimetres.


If a rectangle measuring $5$5 cm by $100$100 cm has an area of $500$500 cm2, it is easy to fall into the trap of thinking this must be the same as $5$5 m2. There's $100$100 cm in $1$1 m, right? Well, yes, but we're not talking about centimetres (cm) and metres (m) now, we're talking about cm2 and m2. That changes things! You'll see more about this later, but for now, don't fall into the trap!

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