10.07 Find areas

We've used squares and rectangles to help us  compare areas  . Let's try this problem to review.

Examples

Example 1

Which shape has the smallest area?

A

B

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.

Watch question walkthrough

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.

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

Examples

Example 2

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

Each grid square represents 1 square unit.

Worked Solution

Create a strategy

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

Apply the idea

There are 32 shaded squares.

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

Watch question walkthrough

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.

Examples

Example 3

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

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.

Apply the idea

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

\displaystyle \text{Area}	\displaystyle =	\displaystyle 2 + 2	Add all the squares
	\displaystyle =	\displaystyle 4 \text{ square units}

Watch question walkthrough

This video shows us how to use unit squares to find the area.

Examples

Example 4

Find the area of the shape below.

Worked Solution

Create a strategy

Count the total number of squares.

Apply the idea

There are 5 squares inside the shape.

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

Watch question walkthrough