# Use Area and Volume Formulae

In this worksheet, students will be asked to find the volume of cubes and cuboids and the area of rectangle and parallelograms.

Key stage:  KS 2

Curriculum topic:   Measurement

Curriculum subtopic:   Use Area/Volume Formulae

Difficulty level:

### QUESTION 1 of 10

In this activity, you will be challenged to work out volume and area of different shapes.

Volume

Remember, volume is measured in cubic units, e.g. 1 cm³ or 1m³.

We need to know the following formulae to work out the volumes of these 3D solid shapes.

Cube

You must know the side length.

Remember, the length, the width and the height will all be equal to the side length because this is a cube.

Volume of cube = side length x side length x side length.

Cuboid

You must know:

The length

The width

The height

Volume of cuboid = length x width x height

Area

Remember area is measured in square units for example, m² or cm².

Rectangles

You must know:

The base length.

The perpendicular height from the base to the top.

Area of rectangle = base x height.

Parallelogram

You must know:

The base length

The perpendicular height from base to top (not the slant height)

Area of parallelogram = base x height

Triangle

You must know,

The base length

The perpendicular height from the base to the apex (not the slant heights)

Area of triangle = 1/2 base x height

Or

Area of triangle = base x height ÷ 2

Want to understand this further and learn how this links to other topics in maths?

Why not watch this video?

What is the area of this rectangle? Give your answer without the squared sign.

45 cm²

450 cm²

59049 cm²

What is the area of this triangle?

60 cm²

600 cm²

255 cm²

What is the volume of the cube?

729 cm³

81 cm³

730 cm³

731 cm³

What is the volume of the cuboid?

14m³

12m³

13m³

11m³

Each side of this cube is 1mm long.

What is the volume?

14m³

12m³

13m³

11m³

Each side of this cube is 3 cm long.

What is the volume?

14m³

12m³

13m³

11m³

The area of this parallelogram is 20 cm².

The base is 4 cm, what must the height be?

The area of this triangle is 17.5m².

The base of the triangle is 7m.

What is the height of the triangle?

"In Maths, we only need to know the length of any two sides to calculate the area of a triangle."

Is Sam correct or incorrect?

Correct

Incorrect

Ahmed makes this statement, "I won't be able to find the volume of this cube as I don't know the width or the height."

Is Ahmed correct or incorrect?

Correct

Incorrect

• Question 1

What is the area of this rectangle? Give your answer without the squared sign.

45 cm²
EDDIE SAYS
Remember, to work out the area of a rectangle, you must calculate base x height. 5 x 9 = 45 cm²
• Question 2

What is the area of this triangle?

60 cm²
EDDIE SAYS
The rule to find the area of a triangle is either ½ x base x height OR base x height ÷ 2. ½ x 15 x 8 = 60 cm² Or, 15 x 8 = 120 120 ÷ 2 = 60 cm²
• Question 3

What is the volume of the cube?

729 cm³
EDDIE SAYS
To find the volume of a cube, we have to remember to use the formula, side length x side length x side length. The calculation we needed was: 9 x 9 x 9 = volume 9 x 9 = 81 x 9 = 729 cm³
• Question 4

What is the volume of the cuboid?

12m³
EDDIE SAYS
How did you get on? These are tricky questions as there are lots of rules to remember. When finding the volume of a cuboid, remember the rule of: length x width x height The calculation needed is: 6 x 1 x 2 = 6 x 2 = 12m³
• Question 5

Each side of this cube is 1mm long.

What is the volume?

EDDIE SAYS
So, the same rule for finding the volume of a cube applied. Side length x side length x side length. The calculation was straightforward: 1 x 1 x 1 = 1mm³
• Question 6

Each side of this cube is 3 cm long.

What is the volume?

EDDIE SAYS
Again, we needed to use the same rule for finding the volume of a cube. Side length x side length x side length. The calculation was 3 x 3 x 3 = ? cm ³ 3 x 3 = 9 x 3 = 27 cm ³
• Question 7

The area of this parallelogram is 20 cm².

The base is 4 cm, what must the height be?

EDDIE SAYS
To solve this question, we have to remember that to find the area of a parallelogram, we multiply the base by the height. We have been told the area is 20cm² and the base is 4cm. To find the height, we will need to do the inverse operation, 20 ÷ 4 = 5cm.
• Question 8

The area of this triangle is 17.5m².

The base of the triangle is 7m.

What is the height of the triangle?

EDDIE SAYS
Here is how to solve this problem: We know one way to find the area of a triangle = ½ x base x height So ½ x 7 = 3.5 Divide the area by 3.5 17.5 ÷ 3.5 = 5 So, the height is 5cm. Feel free to write out your working out with a pencil and paper.
• Question 9

"In Maths, we only need to know the length of any two sides to calculate the area of a triangle."

Is Sam correct or incorrect?

Incorrect
EDDIE SAYS
Sam is incorrect, it's not enough to know any two sides of the triangle, we need to know the base and the perpendicular height!
• Question 10

Ahmed makes this statement, "I won't be able to find the volume of this cube as I don't know the width or the height."

Is Ahmed correct or incorrect?

Incorrect
EDDIE SAYS
Ahmed is incorrect. He doesn't need the measurements of the other sides as it is a cube and all of the edges are equal. The width would be 5cm and the height would be 5cm. Therefore, the volume of the cube is 125cm³.
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