Triangular prism

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

3D shapes

Area of a triangle

Area of a rectangle Substituting into formulae

This topic is relevant for:

Here we will learn about triangular prisms, including nets of triangular prisms and volume and surface area of triangular prisms.

There are also triangular prism worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

A triangular prism is a polyhedron (3D shape made from polygons) consisting of two triangular ends connected by three rectangles. The triangular ends of a triangular prism are congruent (exactly the same).

E.g.

A face of a 3D shape is a flat surface.

Triangular prisms have a total of 5 faces – 2 triangular faces and 3 rectangular faces. The triangular faces of a triangular prism are congruent.

An edge of a 3D shape is a straight line between two faces.

Triangular prisms have 9 edges:

A vertex is a point where two or more edges meet.

Triangular prisms have 6 vertices:

A net of a three-dimensional shape is the 2 dimensional shape it would make if it were unfolded and laid flat. Nets can be folded up to make the 3D shapes.

We can label the vertices (corners) of a prism to help us identify certain edges or faces.

E.g.

Using this labelling we can identify lengths,

E.g. the length AB:

We can also identify faces,

E.g. the face ABC:

The volume of a triangular prism is how much space there is inside of the shape.

To calculate the volume of a triangular prism we find the area of the triangular cross-section and multiply it by the length of the prism (or height of the prism).

text{Volume of a triangular prism } = text{ Area of triangular cross section } times text{ length}

E.g.

Find the volume of the right triangular prism (so called because the triangular faces include a right angle.

Volume is measured in cubic units (e.g. mm^3, cm^3, m^3 etc).

Step-by-step guide: Volume of a triangular prism

Get your free triangular prism worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Get your free triangular prism worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Work out the volume of the triangular prism

The base of the triangle is 10 cm .

The height of the triangle is 4 cm.

The area formula for a triangle is:

begin{array}{l} text{Area of triangle }=frac{1}{2} times b times h\ text{Area of triangle }=frac{1}{2} times 10 times 4\ text{Area of triangle }=20 end{array}

2Multiply the area by the length of the triangular prism.

The volume formula is:

begin{aligned} &text{Volume of triangular prism } = text{ Area of triangular cross section } times text{ length} \ &text{Volume of triangular prism } = 20 times 15 \ &text{Volume of triangular prism } = 300 end{aligned}

3Include the units.

The measurements on this triangular prism are in cm so the volume will be measured in cm^3 .

Volume = 300 cm^3

The surface area of a triangular prism is the total area of all of the faces.

To work out the surface area of a triangular prism, we need to work out the area of each face and add them all together.

Lateral faces are all of the faces of an object excluding the top and the base. For a triangular prism the top and the base are triangles and the lateral faces are rectangular sides. The lateral surface area is the total area of the rectangular sides

The triangular faces of a triangular prism are congruent (exactly the same) but, unless the triangle is an isosceles triangle or an equilateral triangle, the rectangles are all different.

E.g.

Total surface area =168; cm^2

Since it is an area, surface area is measured in square units (e.g. mm^2, cm^2, m^2 etc).

Step-by-step guide: Surface area of a triangular prism

Work out the surface area of the triangular prism

2 Add the five areas together.

24+24+24+32+40=144

3Include the units.

The measurements on the triangular prism are in mm therefore the total surface area of the triangular prism = 144mm^2 .

You should always include units in your answer.
Volume is measured in units cubed (e.g. mm^3, cm^3, m^3 etc).
Surface area is measured in units squared (e.g. mm^2, cm^2, m^2 etc)

You need to make sure all measurements are in the same units before calculating volume.
E.g. You can’t have some measurements in cm and some in m

Be careful to apply the correct prism related formula to the correct question type.

Volume and surface area are different things – volume tells us the space within the shape whereas surface area is the total area of the faces. To find surface area, work out the area of each face and add them together

In surface area questions, we need to know all three side lengths of the triangle however we only need the base and the height to calculate the area of the triangle.

1. Work out the volume of the triangular prism

begin{aligned} text{Volume of triangular prism }&=9 times 8\ &=72mathrm{cm}^{3} end{aligned}

2. Work out the volume of the triangular prism. Give your answer in mm^3

Notice that we have measurements in mm and cm. We can convert the measurements in cm to mm.

1cm = 10mm, 1.1cm = 11mm

Now we can work out the volume:

begin{aligned} text{Area of triangle }&=frac{1}{2} times 10 times 11\ &=55 end{aligned}

begin{aligned} text{Volume of triangular prism }&=55 times 6\ &=330 mathrm{mm}^{3} end{aligned}

3. The volume of this prism is 96 ; cm^2. Work out the height, h , of the prism.

begin{aligned} text{Volume of triangular prism }&=2h times 8\ 96 &= 16h\ 6&=h end{aligned}

The height is 6cm.

4. Work out the surface area of the triangular prism

Work out the area of each face:

begin{aligned} &text{Face} quad quad quad quad quad quad quad quad text{Area} \ &text{Front} quad quad quad quad quad quad frac{1}{2} times 8 times 6 = 24 \ &text{Back} quad quad quad quad quad quad quad quad ; 24 \ &text{Bottom} quad quad quad quad quad quad 13 times 8=104\ &text{Left side} quad quad quad quad quad ; 13 times 6=78\ &text{Right side} quad quad quad quad ;;; 13 times 10=130 end{aligned}

text{Total surface area }=24+24+104+78+130=360mathrm{m}^{2}

5. Work out the surface area of the triangular prism

Work out the area of each face:

begin{aligned} &text{Face} quad quad quad quad quad quad quad quad text{Area} \ &text{Front} quad quad quad quad quad quad frac{1}{2} times 5 times 5 = 12.5 \ &text{Back} quad quad quad quad quad quad quad quad ; 12.5 \ &text{Bottom} quad quad quad quad quad quad 9 times 7.1=63.9\ &text{Left side} quad quad quad quad quad ; 9 times 5=45\ &text{Right side} quad quad quad quad ;;; 9 times 5=45 end{aligned}

text{Total surface area }=12.5+12.5+63.9+45+45=178.9mathrm{cm}^{2}

6. Work out the surface area of the triangular prism. Give your answer in cm^2.

Notice that we have measurements in cm and m. We have been asked for the answer in cm^2 so we need to convert m to cm:
1.5m=150cm.

Now we can work out the area of each face:

begin{aligned} &text{Face} quad quad quad quad quad quad quad quad text{Area} \ &text{Front} quad quad quad quad quad quad frac{1}{2} times 60 times 35 = 1050 \ &text{Back} quad quad quad quad quad quad quad quad ; 1050 \ &text{Bottom} quad quad quad quad quad quad 150 times 60=9000\ &text{Left side} quad quad quad quad quad ; 150 times 35=5250\ &text{Right side} quad quad quad quad ;;; 150 times 69.5=10425 end{aligned}

text{Total surface area }=1050+1050+9000+5250+10425=26775mathrm{cm}^{2}

1. Work out the volume of the triangular prism

(2 marks)

(1)

text{Volume of triangular prism: } 70 times 20 = 1400 mathrm{mm}^{3}

(1)

2. (a) Which of these is a net of a triangular prism?

(b) What would the surface area of the triangular prism be?

(3 marks)

(a) A

(1)

(b)

text{Triangles: } frac{1}{2} times 3 times 4 = 6 mathrm{cm}^{2}

(1)

text{Rectangles: } 12 times 5 =60, 12 times 4 = 48, 12 times 3 = 36

(1)

text{Surface area: }6+6+60+48+36=156mathrm{cm}^{2}

(1)

3. This triangular prism has a volume of 300cm^3. Work out the surface area of the prism.

(5 marks)

(1)

300=30 times text{length}

(1)

text{length } =10cm

(1)

text{Surface area }= 30+30+50+120+130

(1)

text{Surface area }=360mathrm{cm}^{2}

(1)

You have now learned how to:

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths revision programme.