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Australia
Year 4

8.04 Find areas using a grid

Lesson

Are you ready?

Let's try this problem to review how to  compare the area  of shapes.

Examples

Example 1

Which shape has the smallest area?

A
The image shows a irregular shape. Ask your teacher for more information.
B
The image shows a irregular shape. Ask your teacher for more information.
Worked Solution
Create a strategy

Choose the shape that takes up less space.

Apply the idea

The shape in option A is taking up less space than the shape in option B.

The shape that has the smallest area is option A.

Idea summary

When comparing areas of shapes, the shape that takes up less space is the smallest.

Compare area

We can measure area in shapes such as squares and rectangles, but what about different shapes?

To help us measure the area of shapes like the ones pictured below, we can use square units.

The image shows 3 different shapes on a grid. Ask you teacher for more information.

In this video, we look at how to calculate the area of shapes similar to those in the picture shown.

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Examples

Example 2

Find the area of the shape by counting the number of grid squares it covers.

A grid of squares with 32 squares being shaded. Ask your teacher for more information.

Each grid square represents 1 square unit.

Worked Solution
Create a strategy

Count the total number of the shaded squares to find the area.

A grid of squares with 32 squares being shaded. Ask your teacher for more information.
Apply the idea

There are 32 shaded squares.

\text{Area}=32 \text{ square units}

Idea summary

To find the area of a shape on a grid, we can count the number of unit squares inside the shape.

Different shapes

Sometimes we have unusual shapes but we can still work out the area of these shapes by counting the number of square units inside. We can also work out the area of triangles.

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Examples

Example 3

Find the area of the shape by counting the number of grid squares it covers.

A grid of squares with a shaded triangle on it. Ask your teacher for more information.

Each grid square represents 1 square unit.

Worked Solution
Create a strategy

Count the total number of fully shaded squares and combine the half shaded squares to make 1 square unit.

A grid of squares with a shaded triangle on it. Ask your teacher for more information.
Apply the idea

There are 2 shaded squares and 4 halves. The 4 halves can be combined to make 2 more shaded squares:

A grid of squares with a shaded square on it. Ask your teacher for more information
\displaystyle \text{Area}\displaystyle =\displaystyle 2 + 2Add all the squares
\displaystyle =\displaystyle 4\, \text{square units}
Idea summary

We can combine half square units inside a shape to make whole square units in order to find the area.

Area of shapes

This video shows us how unit squares can help us find the area of a shape.

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Examples

Example 4

Find the area of the shape below.

The image shows an L shape made up of 5 squares. Ask your teacher for more information.
Worked Solution
Create a strategy

Count the total number of squares.

Apply the idea

There are 5 square inside the shape.

\text{ Area }= 5\, \text{units}^2

Idea summary

To find the amount of space a shape takes up, we can use a unit square.

Outcomes

ACMMG290

Compare objects using familiar metric units of area and volume

ACMMG087

Compare the areas of regular and irregular shapes by informal means

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