Maths

Area and perimeter

The squares on this grid are 1cm x 1cm, so the area of each
square is 1cm^{2}.

What is the area of the shape on this grid?
The shape covers 8 squares, so the area is 8cm^{2}.

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:

- Answer
The answer is 10cm

^{2}.

**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 30cm^{2}. So the area of the triangle will be half of this. The area of the triangle is 15cm^{2}.

- Question
Calculate the area of this triangle using the grid.

- Answer
The area is 10cm

^{2}.The area of the rectangle is 20cm

^{2}, then we half it.

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.

The formula for the area of a rectangle is:

**Area = base x height.**

The area of this rectangle is 72cm^{2} (12 x 6 = 72).

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 20cm^{2}:

^{1}/_{2}(10 × 4) = 20

Now try these questions.

- Question
Find the area of the following shape:

- Answer
The answer is 77cm

^{2}.You need to multiply 7 by 11.

- Question
Find the area of the following shape:

- Answer
The answer is 14cm

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

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?

- Answer
The answer is 35cm

^{2}.To find the area, you need to divide the shape into a rectangle and a triangle:

The area of the rectangle is 5 × 4 = 20cm

^{2}.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) = 15cm^{2}The total area is 20 + 15 = 35cm

^{2}.

Remember: in these diagrams **h** is the perpendicular height.

The area of a parallelogram is b × h

The area of a trapezium is ^{1}/_{2} × h × (a + b)

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.

- 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

**13cm**^{2}Remember the units for area are different to the units for perimeter.

**Now try a **Test Bite