Maths

Area and perimeter

Finding the areas of shapes on grids by counting squares

The squares on this grid are 1cm x 1cm, so the area of each square is 1cm2.

What is the area of the shape on this grid? The shape covers 8 squares, so the area is 8cm2.

Being well-organised helps. One idea is to count down the rows and tick them off as you do so. This will help to avoid mistakes.

Question

Sometimes the shapes are more complex. See if you can find the area of this shape:

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Answer

The answer is 10cm2.

Area of triangles

You can find the area of triangles by following these steps:

  • Make the triangle into a rectangle.
  • Count the squares in the rectangle.
  • Halve the number of squares in the rectangle (i.e., divide them by 2).

To find the area of this triangle,

you first make it into a rectangle:

The area of the rectangle is 30cm2. So the area of the triangle will be half of this. The area of the triangle is 15cm2.

Question

Calculate the area of this triangle using the grid.

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Answer

The area is 10cm2.

The area of the rectangle is 20cm2, then we half it.

Calculating the areas of rectangles and triangles

You have learnt how to find the areas of rectangles and triangles by counting squares. However, sometimes you will have to calculate the areas of shapes without using a grid.

Rectangles

The formula for the area of a rectangle is:

Area = base x height.

The area of this rectangle is 72cm2 (12 x 6 = 72).

Triangles

To find the area of a triangle, you use the formula:

Area = 1/2 × base × height

Remember another way to find the area of a triangle, first make it into a rectangle, then divide by 2.

The area of this triangle is 20cm2:

1/2(10 × 4) = 20

Activity

See how areas work in this activity.

Now try these questions.

Question

Find the area of the following shape:

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Answer

The answer is 77cm2.

You need to multiply 7 by 11.

Question

Find the area of the following shape:

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Answer

The answer is 14cm2.

If you had problems, remember that the rule is to multiply 7 by 4, then divide by 2.

More complex shapes

You have learnt how to find the area of a rectangle and a triangle. We are now going to look at finding the area of a more complex shape.

Question

What is the area of this shape?

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Answer

The answer is 35cm2.

To find the area, you need to divide the shape into a rectangle and a triangle:

The area of the rectangle is 5 × 4 = 20cm2.

The base of the triangle is calculated by subtracting the base of the rectangle (4cm) from the total length of the shape (10cm). So 10cm - 4cm = 6cm.

The area of the triangle is 1/2(5 × 6) = 15cm2

The total area is 20 + 15 = 35cm2.

Area of a parallelogram and trapezium

Remember: in these diagrams h is the perpendicular height.

Parallelogram

The area of a parallelogram is b × h

image: parallelogram

Trapezium

The area of a trapezium is 1/2 × h × (a + b)

image: trapezium

Perimeters

The perimeter of a shape is the distance around it.

The perimeter of this rectangle is 20cm. If we start from A and move around it in a clockwise direction, we travel a distance of 6cm + 4cm + 6cm + 4cm = 20cm.

Question

Sometimes the shapes are more complex. Try to find the perimeter and area of this shape. All the squares are 1cm by 1cm.

An irregular shape drawn on graph paper

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Answer

The perimeter of the shape is 18cm.

If you did not get this right, mark the side where you start counting and make sure you don't count any square twice

The area of the shape is 13cm2

Remember the units for area are different to the units for perimeter.

Activity

Play this activity to investigate area and perimeter.

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