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How to Find the Area of a Shape Which Is Drawn on Squared Paper

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How To Find The Area Of A Shape On Squared Paper

Area is the amount of space contained inside a 2D shape. If the shape is drawn accurately on squared paper, then all you need to do is count the amount of squares that are contained inside the shape. To keep track of how many squares you have counted try putting a dot inside each square (or put a number inside each square). Let’s take a look at some examples on working out areas of 2D shapes.

Example 1

Work out the area of this shape which is drawn on centimetre squared paper.

how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

All you need to do is count the amount of squares inside the shape.

There are 5 squars on the top row, 5 squares on the middle row, and 5 squares on the bottom row of the shape.

If you now add all these up then you get a total of 15 squares which are inside the shape.

So the area of the shape is 15 cm².

A good tip is to put circles or dots inside the shape so that you can keep track on the squares that you have counted. Alternatively if you can fit numbers inside each square if you can write small.

how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

Example 2

Work out the area of this shape which is drawn on centimetre squared paper.

how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

Again, all you need to do is count the amount of squares inside the shape.

Follow the method in the previous example and put dots in each square to help keep track on which squares have been counted. It doesn't matter where you start off or which order you count the squares in.

Altogether you should have counted 35 squares.

So the area of the shape is 35 cm².

how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

Example 3

Work out the area of this shape which is drawn on centimetre squared paper.

how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

Like the last two examples, all you need to do is count the amount of squares inside the shape.

However, the shape contains some half squares, but 2 of these can be put together to make a whole square.

First count the amount of full squares by putting dots in each of these square.

Altogether there should be 11 full squares, and there should be 3 half squares that are left over.

Two of these half squares can be put together to make a whole square and 1 half square is left over.

Therefore the total are of the shape is:

11 + 1 + ½ = 12 ½ cm²


how-to-find-the-area-of-shape-by-counting-the-squares-year-6-maths

Once you have mastered finding the area of shapes on squared paper, you can then find move on to working out the areas of shapes that are not drawn on squared paper. To find the area of shapes that are not drawn not on squared paper you will need to learn formulae for each shape.

So for example, you can work out the area of a square or rectangle by multiplying the length of the rectangle by the width of a rectangle. This is much quicker than counting the amount of squares that are inside the shape.

Working out the area of a triangle can be a little harder. This time multiply the base length of the triangle by the perpendicular height and divide the answer by 2. This is because a triangle will take up half the amount of space that a rectangle can contain.

You can also use the formula Pi multiplied by the radius squared to find the area of a circle, as this would be very difficult if you had to find the area if it was draw on squared paper.

In fact, you can work out the area of any shape if you know the correct formulae. Sometimes the shape in question might be made up of 2 or more simple shapes, and you will need to work out the area of each individual shape and then add them up. These are called compound or composite shapes.

So to summarise, the area of any shape can be found by counting the squares that are inside the shape as long as the shape is drawn on squared paper. If the shape is not drawn on squared paper then apply the correct formula for the shape that you have. Also don't confuse area with perimeter, as perimeter is the distance around the outside of the shape and can be found by adding up the side lengths.

Comments

Smarty pants on January 17, 2013:

But this website is good too

Smarty pants on January 17, 2013:

It's very easy to calculate area just ask your teacher or parents if you don't understand

Hettie Marbles on May 14, 2012:

How Do You Find Out Area Without Squares To Count?

Like On SATs You Will Get Shape That You Will Need To Find The Areas Of And You Don't Have Squares To Count With So What Do You Do?

punk3 on December 11, 2011:

can you please put a shape but that has only some parts in half and not a whole square.?