Shapes (2D & 3D)

In your exam, you’ll need to know various shapes and what they look like.

Why?

Because you’re likely going to be asked questions that require knowledge of shapes such as an area or perimeter calculation.

The below is just a quick run through of the shapes and attributes, and we’ll go through the calculation of perimeter and area or volume in more detail in the next checkpoint.

Now, let's go through and talk about the attributes of each of the shapes below (watch video).

In addition to the above shapes, you also have polygons with a certain number of sides (see below).

Aside from the shapes above, you also need to know the various types of 3D shapes like these:

In your exam, the questions that you’ll be asked the require knowledge of shapes are likely to be area or perimeter questions. Rarely are you asked to identify a shape, but you do need to be able to identify a shape in order to answer other questions, so that’s what you’ll do in the following section.

Identify shapes

I am a 3D solid with 6 equal faces

Which shape am I?

A rectangular solid B cube C Cone D cylinder

I am a 3D solid with 1 face

Which shape am I?

A sphere B cube C Cone D cylinder

I am a polygon with 3 sides.

Which shape am I?

A cylinder B triangle C square D rectangle

I am a polygon with 4 sides with no right angles and with only 1 set of parallel lines.

Which shape would I most likely be?

A square B rectangle C parallelogram D trapezoid

Key Rules to remember

• Know the attributes and names of 2D & 3D shapes.
• While the identification of shape questions are not the most common type of questions, you need to know them because they are in other types of questions.

Area, perimeter and volume

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

Angles

When dealing with angles it’s important to see the bigger picture – that is, angles are parts of a whole, and that whole is 360 degrees.

Let's look at types of angles and what they look like.

Orias / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0). Built upon by Exam Success.

Important tips to remember when dealing with angles are:

• Right angle – lines that intersect are perpendicular. A little square represents a right angle.
• Straight angle – Angle in a straight line and is 180 degrees (2 sides of the straight line add to 360 degrees).
• Angles around a point add up to 360 degrees.
• Angles in a square add up to 360 degrees.
• Angles in a triangle add up to 180 degrees.
• Complementary angles are angles that together add up to 90°.
• Supplementary angles are angles that together add up to 180°.

Parallel Lines

Interestingly, there are some rules with angles when parallel lines cross. These are:

• Corresponding angles are equal (for examples, a = e).
• Alternate interior angles are equal (d = f).
• Same side interior angles add to 180° if on a straight line.

Example Question/s

Watch video for explanation of the following question/s:

In the figure below what is the value of x?

A 25° B 45° C 30° D 90°

Find the value of angle y in the figure below.

A 110° B 50° C 70° D 30°

a° = ?

A 75° B 70° C 105° D 110°

x° = ?

A 90° B 45° C 135° D 180°

Key Rules to remember

• Know the names of angles and that complementary angles add up to 90° while supplementary angles add up to 180°.
• The little square represents a right angle (90°).
• Internal angles of a triangle add up to 180° while internal angles of a square or rectangle add up to 360°.
• Know the rules with parallel lines.

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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