NZ Level 4
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Area of Rectangles and Squares
Lesson

The space inside a rectangle

To find out how much space is inside a rectangle (or square, which is a special kind of rectangle), its area, you could fill the shape with unit squares, and count the unit squares.  Another way though, is to use this rule:

Area = Length × Width

The thing is, rectangles have two pairs of equal sides, so we only need two measurements! This video shows you how to find the length and width, and then you can use multiplication to find the area. With a square, we only need one measurement.

Worked examples

Question 1

Find the area of the rectangle shown.

What if we know the area?

Remember how we only needed to know the length and width to work out the area? Sometimes we might know the area of a rectangle, and either the length or width. Using division, we can work out the missing value! In fact, since a square has $4$4 equal sides, if we know its area, we can work out how long those sides are. How amazing is that! Let's see how it works in this video.

Worked Examples

Question 2

Find the perimeter of a square whose area is $49$49cm2.

 

Give it a go!

Here's an applet that lets you make some changes. You can change the length and/or width, and see how the area changes. You can also hide the length or width and see how you go working it out.

The area of things!

Once you know how to calculate the area of a rectangle, or find the missing length or width (or sides, if it's a square), you can work out the area of rectangles to do things like:

  • covering your desk with plastic, to protect it,
  • painting the top of your desk, to change the colour, or 
  • putting a rug down on the floor of your bedroom or playroom.

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

 

Worked Examples

Question 3

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

  1. What is the area of the driveway?

Off you go!

Now you can explore some problems where you may need to work through a couple of steps. In this set of videos, you can see what steps you may need to go through, to solve an everyday problem. 

Worked Examples

Question 4

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.

Remember!

It all comes back to area being equal to length × width, no matter which unit of measurement you're using, and expressing the answer as squared units. For squares, length and width are equal, so we can just call them sides, and area is side × side.

Outcomes

GM4-3

Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids

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