Math Help: What Are Area and Perimeter? How to Work out the Area and Perimeter of a Compound Shape

Updated on February 24, 2017

What Is Area?

Area is the amount of surface the 2D shape covers. It is measured in square units.

What Is Perimeter?

The perimeter is the total distance around the outside of the 2D shape. You calculate it by adding all together all the lengths of the shape.

How Can I Remember What Area Is?

Match the word with words you know.

The playground area is where you play, so the area is the space in shape.

The area on a football pitch is where the goalkeeper is allowed to pick up the ball. The area is the inside of this rectangle, so the area is the space in shape.

How Can I Remember What Perimeter Means?

We sing a song as we walk around the edges of the tables in our room.

The tune is to the song "Here we go round the mulberry bush."

"Here we go round the perimeter fence, the perimeter fence, the perimeter fence. Here we go round the perimeter fence, add up all the sides."

How Can I Remember the Difference Between Area and Perimeter?

Make a chant up or song to remember the differences:

Area is inside,

Area is inside

you count the squares or multiply

Multiply the length times width

Perimeter's around the edge,

Perimeter's around the edge,

You add up all the sides

You add up all the sides.

As a teacher I am interested to know which idea you like better.

Which way do you think is best to remember the difference between area and perimeter?

See results

A Second Way to Remember the Difference

A nice simple way is to remember these:

Area = all (a=a)

Perimeter = rim

Another Great Way, Although Cheeky, of How to Remember the Difference of Area and Perimeter

Area
Perimeter
Area = side x side
Perimeter = side + side + side + side
A=SS
P = S + S + S + S
ASS
PSSSS

What Is a Compound Shape?

A compound shape is a shape that has an irregular arrangement of sides or angles and must be broken down into simpler shapes before you can work out the area or perimeter.

It is a useful way of looking at shapes that are not straightforward to deal with. In upper KS2 and KS3 children look at working out the area of a compound shape that is made up of two or more rectangles.

So How Do You Work out the Area of the Compound Shape Above?

Remember the area is the space inside. We know that to work out a rectangle by multiplying the length by the width.

So when it comes to compound shapes, if we split the shape up into rectangles, then it will become a lot easier to find the area of the total shape.

Above we can see that if we split the compound shape into two rectangles, the area is the same.

So we find the area of both rectangles and then add them up.

What Are the Steps I Should Follow to Find the Area of a Compound Shape?

  1. Split your compound shape into a series of rectangles. It is better to actually draw these lines on so you can see exactly what you need to work out.
  2. Work out the missing lengths you need around the edge.
  3. Work out the area of each separate rectangle. (Remember that this is done by multiplying the length by the width.)
  4. Add these separate areas for each rectangle up together to find the total area of the compound shape.

Example 1 of how to do it:

Example One Shows Some Techniques to Work out the Area of a Compound Shape

The first and second way is to split the compound shape into two rectangles. It is done differently with both examples, but the basic maths is the same.

You work out the area of each rectangle and then add them together.

The last method to work out the area for this compound shape is a little different. Instead of adding the area of two rectangles up like the previous examples you can do something very different:

  • Work out the area a large shape around the compound shape. In this case, you can do 7x7 to work out the area of the compound shape and the small area of a shape that has been cut out!
  • This is represented by the green lines on the example.
  • Next, you need to work out the area of the shape that is cut out. In this case, it is 3x3.
  • Last, of all you take the area of this cutout shape and take it away from the large rectangle. 49 - 9 = 40cm squared.

Use the Method That You Can 'See' Better

If you can see how to split up a compound shape into two or more rectangles easier than spotting the cutout method then follow that rule.

Example 2 of how to do it:

This Is What the Website Looks Like

How to Work out the Perimeter of a Compound Shape

This works differently to finding out the area of a compound shape in that you do not need to divide the shape into rectangles.

What you need to do is add up each individual side of the shape.

You will obviously need every measurement for each side to do this, so this may be the first thing you need to work out.

Steps to Working out the Perimeter of a Compound Shape:

  1. Work out any missing length for the sides.
  2. Add up every side to work out the perimeter of the compound shape.

An Example:

In this example you need to add up all the sides:

5+5+3+3+2+2 = 20cm

(Note, it is a good idea to cross off each length as you go along, so you make sure you do count all the sides and also that you do not add a length twice. This is because compound shapes can become very complicated so you can add up a lot more sides than the example given here.)

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