Let's extend our knowledge of shapes by looking into a common tested area: area, perimeter and volume.

How to calculate

You should know the following calculations.

Area

Area is the space inside a closed shape. It is expressed in units squared.

• Square/Rectangle = (L x W)
• Triangle = (L x W) ÷ 2
• Irregular shapes – cut the shape to make smaller shapes and if possible, apply formulas and then total

Perimeter

The perimeter is the outline. To calculate this, the length of the sides of a shape should be added together. It is expressed in the units requested e.g. cm, metres etc…

Can you find the perimeter and volume of the following shape? See video for explanation.

Volume

Volume is the ‘fill’ of a shape and is commonly expressed in units cubed. It can also be expressed in other units that are purposely ‘built’ for volume such as ml and litres.

One of the things to note with volume is that the ‘fill’ of something is the total space less the ‘unfilled’ part, to get the ‘fill’. Knowing this allows you to problem solve and work out different angles when you get tricky questions.

The volume of a cube is L x W x H.

Other formulas can be seen here:

Example Question/s

Watch video for explanation of the following question/s:

The area enclosed in this shape is 16 square units.

What is the area of the shaded shape?

A 32 square units B 58 square units C 14 square units D 24 square units

The perimeter of the shape is:

A 56 cm B 78 cm C 54 cm D 92 cm E None of these

If Density = Mass ÷ Volume, what is the mass of the solid in the diagram if its density is 400kg/metres cubed?

A 9700 kg B 4200 kg C 10800 kg D 8700 kg E None of these

The next 2 questions refer to the following information:

James has a rectangular plot. He wants to divide it into three triangular plots.

What will be the total area of the smaller triangular plot?

A 9 square meters B 4 square meters C 6 meters D 2 meters

What is the total area of the R and L plot only?

A 12 square meters B 24 square meters C 54 meters D 72 meters

Key Rules to remember

• Area of square/rectangle = (L x W)
• Area of triangle = (L x W) ÷ 2
• Area of irregular shapes – cut the shape to make smaller shapes and if possible, apply formulas and then total
• To get perimeter – add all sides together
• To get volume of a cube do: l x w x h

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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