Perimeter = distance around the edge.

You could walk around the perimeter.

Don't mix cm with m.

Example

P = 5 + 2 + 2 + 3 + 9 + 3 + 2 + 2 cm

P = 28 cm

Area = floor space covered

You could paint an area.

Don't mix cm,^{2} with m^{2}

1 m^{2} = 100cm x 100cm

= 10000 cm^{2}

Example

Calculate the area of the square

Examples

Calculate the area of the rectangles

Area of a triangle = ½ x base x perpendicular height

Examples

Find the area of the triangle below:

What is the length of the base of the
triangle, if it has an area of 45 cm^{2 }?

Example

Calculate the area of the following kite:

Area of a trapezium = ½ x average of base x perpendicular height

Example

What is the area of this trapezium ?

(Each square represents 1 cm^{2} )

Example

Calculate the area of the parallelogram :

Example

Calculate the area of the rhombus:

( The sizes are for the complete diagonals)

Volume = capacity held

You could fill a volume

Don't mix cm with m.

Notice that for a cuboid

Example

Calculate the volume of the cuboid below:

Example

Converting 1m^{3} to litres

First, convert the units

But 1 cm^{3} = 1 ml and 1000 ml = 1litre

Divide cm^{3} by 1000 for litres.

So 1 000 000 cm^{3} = 1000 litres

1 m^{3} = 1000 litres

A sphere has volume

Where r is the radius of the sphere.

Examples

Calculate the volume of the following sphere.

Give your answer correct to 1 dp and also to 2 sig figs.

Calculate the volume of the following sphere.

Give your answer correct to 1 sig fig.

Calculate the diameter of a sphere which has a volume of 700cm^{3}.

Give your answer correct to 1 dp.

A cone has volume

Where r is the radius of the circular part of the cone and h is the perpendicular height of the cone.

Example

Calculate the volume of an ice cream cone which has a diameter of 4cm and a height of 6cm. Give your answer correct to 1 dp.

How many of these cones can be filled from 1litre of ice cream ?

1000 cm^{3} = 1 l

1000 ÷ 25.1 = 39.84

So 39 cones can be filled from one litre of ice cream.

Example

Calculate the height an ice cream cone which has a diameter of 4cm and a volume of 35ml. Give your answer correct to 1 dp.

The cone is 8.4 cm tall.

Example

Calculate the diameter of an ice cream cone which has a height of 8cm and a volume of 90ml. Give your answer correct to 1 dp.

So Volume = Area x height (or Area x Length if laying down)

Example

What is the volume of a prism
which has an area of 37 cm^{2}
and a height of 4 cm ?

A cylinder is a circular prism,

Example

Calculate the volume of a tin can which has a height of 0.8m and a diameter of 10 cm. Give your answer correct to 1 sigfig.

Example

Calculate the diameter of a tin can which has a height of 8cm and a volume of 90ml. Give your answer correct to 1 dp.

The volume of any pyramid is given as

where A is the area of the base of the pyramid and h is its height.

Examples

What is the volume of this squared based pyramid ?

What is the volume of this rectangular based pyramid ?

What is the volume of this triangular based pyramid ?

The surface area is the total external area

of the shape.

Example

Find the surface area of the cuboid :

This shape has 6 faces

2 faces have area 6cm x 4cm

2 faces have area 6cm x 2cm

2 faces have area 2cm x 4cm

2 x 6cm x 4cm = 48 cm^{2}

2 x 6cm x 2cm = 24 cm^{2}

2 x 2cm x 4cm =__ 16 cm ^{2}__

Surface Area = 88 cm

Surface Area ≠Volume

Cut into convenient shapes

Find missing dimensions

Calculate individual areas

Calculate total

Remember

all dimensions must have the same units !

Example

A shape = A 1 + A 2

A 1 = 5x2 = 10 cm^{2}

A 2 = 3x9 = 27 cm^{2}

A shape = 37 cm^{2}

Cut into convenient shapes

Find missing dimensions

Calculate individual areas

Calculate total

Example