6th Grade

Welcome to our Surface Area Worksheet 6th Grade collection.

Here you will find a range of surface area worksheets to help you learn how to find the surface area of a range of different nets including cubes, prisms and pyramids.

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This page is all about finding the surface area of a range of different 3d shapes, drawn as nets.

The 3d shapes include:

- cubes and cuboids;
- triangular prisms;
- square pyramids.

Some of the sheets also involve working out the lengths of an unknown side, when the surface area is given.

Want to test yourself to see how well you have understood this skill?.

- Try our NEW quick quiz at the bottom of this page.

What is the surface area of a 3d shape?

The surface area of a 3D shape is the sum of the areas on all of the outer faces.

How to find the surface area of a 3d shape?

To find the surface area of a 3d shape, we need to find the area of each of the faces.

To find the area of square and rectangular faces, we just need to multiply the adjacent sides together.

To find the area of triangular faces, we need to multiply the base by the perpendicular height and then halve the answer.

Example 1) Find the surface area of the cube below.

The width of one side of each square face is 4cm.

So the area of each square face is 4 x 4 = 16 cm^{2}.

The cube has 6 identical square faces, so the total surface area is 16 x 6 = 96 cm^{2}.

Example 2) What is the surface area of the cube below.

The width of one side of each square face is 1 ½ inches.

So the area of each square face is 1 ½ x 1 ½ = 2 ¼ in^{2}.

The cube has 6 identical square faces, so the total surface area is 2 ¼ x 6 = 13 ½ in^{2}.

Example 3) Find the surface area of the cuboid below.

There are 6 faces in the cuboid, with 3 identical faces each repeated twice.

Face1: 6cm by 4cm. Area = 6 x 4 = 24 cm^{2}

Face2: 6cm by 3cm. Area = 6 x 3 = 18 cm^{2}

Face3: 3cm by 4cm. Area = 3 x 4 = 12 cm^{2}

The surface area of the cuboid is (Area of Face1 x 2) + (Area of Face2 x 2) + (Area of Face3 x 2)

So the surface area of this cuboid is (24 x 2) + (18 x 2) + (12 x 2) = 48 + 36 + 24 = 108 cm^{2}.

Example 4) What is the surface area of the triangular prism below.

The triangular prism has 5 faces, two identical triangular faces, and three rectangular faces, two of which are identical.

Face1 (rectangular): 10 in by 5 in. Area = 10 x 5 = 50 in^{2}

Face2 (rectangular): 10 in by 6 in. Area = 10 x 6 = 60 in^{2}

Face3 (triangular): 6 in base and 4 in perpendicular height. Area = ½ x 6 x 4 = 3 x 4 = 12 in^{2}

So the surface area of the triangular prism is (Area of Face1 x 2) + Area of Face2 + (Area of Face3 x 2).

So the surface area is (50 x 2) + 60 + (12 x 2) = 100 + 60 + 24 = 184 in^{2}.

Example 5) Find the surface area of the square pyramid below.

The square pyramid has one square face and four identical triangular faces.

Square Face: 12cm by 12cm. Area = 12 x 12 = 144 cm^{2}

Triangular Face: base: 12 cm perpendicular height: 8 cm. Area: ½ x 12 x 8 = 6 x 8 = 48 cm ^{2}

The surface area of the pyramid is (Area of Square Face) + (Area of Triangular Face x 4)

So the surface area of this pyramid is 144 + (48 x 4) = 144 + 192 = 336 cm^{2}.

These sheets involve working out the surface area of a range of cubes.

The first two sheets involve finding the surface area of the cubes.

The third sheet is harder and also involves finding the length of one side of the square face, when the surface area is given.

These sheets involve working out the surface area of a range of cuboids from their nets.

The first two sheets involve finding the surface area of the cuboids.

The cuboids in the 2nd sheet have fractional length sides.

The third sheet is harder and involves finding the length of one side of the cuboid, when the surface area and two of the other sides are given.

These sheets involve working out the surface area of a range of square pyramids from their nets.

These sheets involve working out the surface area of a range of triangular prisms from their nets.

These sheets involve working out the surface area of a range of different 3d shapes from the sheets above.

Shapes covered: cubes, cuboids, square pyramids and triangular prisms.

This short video walkthrough shows several problems from our Surface Area Cubes Prisms & PyramidsWorksheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

Take a look at some more of our worksheets similar to these.

Here is our range of 6th grade Geometry worksheets including area and perimeter worksheets.

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This quick quiz tests your knowledge and skill at finding the surface area of different 3d nets.

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