Perimeter, Area and Volume Grades F to A. Hyperlinks! Counting Squares Area – working backwards...

Perimeter, Area and Volume

Grades F to A

Hyperlinks!

Counting Squares

Area – working

backwardsCircles

Volume of cuboids

Sectors of circlesSurface area

Volume of prisms

Volume and surface area of complex

shapes

Rectangles and Triangles

Parallelograms and

Trapeziums

Compound Shapes

Success Criteria: Where Are We Now?Level Learning outcomes: R A G

F2 I can find the perimeter and area on a shape by measuring or counting.

E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.

D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms

such as cones and spheres using the formulae.

Area and perimeter by counting and measuring

How do I find the area and perimeter of a shape?

Grade F

What are perimeter and area?

Perimeter is the length around the outside of a shape.

Area is the space inside a shape.

Example

The rectangle has a perimeter of:

The rectangle has a area of:

5 + 3 5 + 3+ = 16cm

5 × 3 = 15cm²

5 + 5 = 15cm²5 +Take note of

the units!

Find the perimeter and area of this rectangle:

Perimeter =

Area =

20cm

24cm²

Rectangles and Triangles

Can I calculate the perimeter and area of a rectangle and triangle?

Grade E

The formulae to remember:•

Two examples:Example 1

Find the area and perimeter of this rectangle:

Area = 8 × 6Area = 48cm²

Perimeter = 8 + 6 + 8 + 6Perimeter = 28cm

Example 2

Find the area of this triangle:

Area = 5 × 12 ÷ 2Area = 60cm² ÷ 2

Area = 30cm²

6cm

8cm

5cm13cm

12cm

Have a go at some:Question 1

Find the area of this triangle:

Question 2

Find the perimeter and area of this rectangle:

10cm

11cm

8cm7cm

Answer: 35cm²Answer:

Area = 88cm²Perimeter = 38cm

Parallelograms and Trapeziums

Can I calculate the area of a parallelogram and trapezium?

Grade D

The formulae:•

Two examplesExample 1

Find the area of this parallelogram:

Area = 7 × 5Area = 35cm²

Example 2

•

7cm

5cm 6cm 5cm

4cm

8cm

Have a go at a couple of questions:Question 1

Find the area of this parallelogram:

Question 2

Find the area of this trapezium:

12cm

8cm10cm 7cm

9cm

11cm

Answer: 96cm²Answer: 70cm²

Circles

Can I find the circumference and area of a circle?

Grade C

Names to do with circles you must remember:

Radius

Diameter

Chord

Tangent

Circumference

Formulae you need to remember:

•

A couple of examplesExample 1

Find the circumference and area of a circle with a diameter

of 10cm to 1 dp.

Circumference = π × 10Circumference = 31.4cm

Area = π × 5²Area = 78.5cm²

Example 2

Find the circumference and area of a circle with a radius of

8cm to 1 dp.

Circumference = π × 16Circumference = 50.3cm

Area = π × 8²Area = 201.1cm²

Some for you to try:Question 1

Find the circumference and area of this circle to 1 dp.

Question 2

Find the circumference and area of a circular pond with a

diameter of 3m to 1 dp.

Circumference = 88.0cmArea = 615.8cm²

Circumference = 9.4mArea = 7.1m²

14cm

Area – Working Backwards

Now you can find the area of shapes, can you find a length having been

given the area?

Formulae Reminder:•

Find the missing lengths:

Area = 48cm²Area = 21cm²

Area = 32cm² Area = 28cm² Area = 113.1cm²

8cm

?cm 7cm

?cm

8cm

9cm

?cm

Diameter = ?Height = ? Height = 4cm

None of these are drawn to

scale

6cm

6cm

4cm

5cm

12cm

Compound Shapes

Can I calculate the perimeter and area of a compound shape?

Grade C

What is a compound shape?

A compound shape is a shape that is made up of lots of different shapes.

The key is to split the complex shape up into simpler shapes, find the areas of the simple

shapes then add your areas together.

An exampleFind the area of this shape:

Split it up!

Area = 40 + 32 = 72cm²

12cm

8cm8cm

3cm

Area = 8×5 = 40cm²Area = 8×4

= 32cm²

Another exampleFind the area of this shape:

Split it up!

Area = 54 + 13.5 = 67.5cm²

3m

9m

6m Area = 9×6 = 54m²

A couple of questions:Question 1

Find the area of this shape:

Question 2

Find the area of this shape:

10m

8m

6cm

12cm

3cm

5cm

Answer: 66cm² Answer: 119.3m²

Volume of Cuboids

Can I calculate the volume of a cuboid?Grade C

How to calculate the volume of a cuboid:

•

An example:

Find the volume of this cuboid:

Volume = 3 × 5 × 4Volume = 60cm³

3cm

5cm4cm

Take note of the units!

Another example, working backwards:

Find the height of this cuboid:

280cm³ = 10 × 7 × hh = 280 ÷ (10 × 7)

h = 4cm

10cm7cm

Volume = 280cm³

Two questions to have a go at:

Question 1Find the volume of this cuboid:

Question 2The tank below contains exactly 100 litres of water. How far up the tank does the water go?

(Hint: 1 litre = 1000cm³)

5cm

8cm

6cm

1m0.5m

0.5m

Answer: 240cm³ Answer: 0.2m or 20cm

Prisms

Can I calculate the volume of a prism?

Grade C

What is a prism?

A prism is a 3D shape that has the same cross-section all the way through.

For example:

Triangular Prism Hexagonal Prism Cylinder

Calculating the volume of a prism:

Find the area of the cross-section then multiply by the length.

Volume = Area of cross-section × length

Two examplesExample 1

•

Example 2

If the volume of this prism is 360cm³ and it is 9cm long,

what is the area of the cross-section?

Area of cross-section = 360 ÷ 9Area of cross-section = 40cm²

8cm

3cm

A couple of questions:Question 1

Find the volume of this triangular prism:

Question 2

A circular pond contains 18,850 litres of water. It has a diameter of 4m. How deep is

the pond if it is a cylinder?(1 litre = 1000cm³)

8cm 12cm

9cm

Answer: 432cm³ Answer: 1.5m or 150cm

Surface Area

Can I calculate the surface area of a cuboid or a triangular prism?

Grade C to B

What is surface area?

The area of all the faces of a 3D shape added together.

You could think of it like this: it is the exact amount of wrapping paper you would need to

wrap your shape up with.

Find the surface area of this cuboid:

Each face you can see has a face exactly the same opposite it.

2 × 4 × 10 = 80cm²2 × 4 × 5 = 40cm²

2 × 5 × 10 = 100cm²Total surface area = 220cm²

4cm

10cm5cm

4cm × 5cm = 20cm²5cm × 10cm = 50cm²

4cm × 10cm = 40cm²

There are two of each size of

rectangle

Find the surface area of these two cuboids:

Cuboid 1

Answer: 258cm²

Cuboid 2

Answer: 192cm²

9cm

5cm6cm

4cm

12cm3cm

A Triangular Prism Example:•

A Cylinder Example:Find the surface area of this cylinder:

It’s two circles and a rectangle (whose length is the circumference of the circle):

Surface area = 2 × π × 4² + 5 × π × 8

Surface area = 226.2cm²

4cm

5cm

The two circles The rectangle

Find the surface area:

Answer: 527.8cm²

12cm

8cm

Sectors of Circles

Can I find the area of a sector and its arc length?

Grade B

What is a sector?

A sector is a fraction of a circle – like a slice of cake or pizza.

It’s point is the centre of the circle.

The arc length is the curved part of the sector.

The formulae:•

Area of a whole circle

Circumference of a whole circle

Angle given for the sector

An exampleFind the area and arc length of this sector.

7cm

7cm50

Area:

Area = 21.4cm²

Arc Length:

Arc Length = 44.1cm

A question for you:Find the area and perimeter of this sector.

(Don’t forget the “straight bits” for the perimeter!)

Area = 15.4cm² Perimeter = 15.7cm

4cm4cm 110

Volume and Surface Area of Complex Shapes

Can I use the formulae to find surface area and volume of cones and

spheres?Grade A

Some formulae for you:

• •

These formulae are at the front of the paper!

And one more…

•

Cone Example:• •

5cm

12cm 13cm

Circular base

Curved surface area

Sphere Example:

• •

r = 6cm

Two questionsQuestion 1

Find the volume and curved surface area of this cone:

Question 2

Find the volume and curved surface area of this sphere:

6cm

8cm 8cm

C.S.A. = 188.5cm² Volume = 301.6cm³

Surface area = 804.2cm² Volume = 2144.6cm³

The frustumA frustum is a cone or pyramid that has had it’s

top chopped off!

Remember: the original cone/pyramid and the cone/pyramid that has been chopped off are similar, mean that the dimensions are in the

same ratio.

Find the volume of the frustum:•

3cm

6cm

5cmDouble the radius, so

double the height

Try this one:

Find the volume of this frustum:

3cm

9cm

8cm

Answer: 980.2cm³

Perimeter, Area and Volume Grades F to A. Hyperlinks! Counting Squares Area – working backwards...

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