area and volume

Area and Volume

Using formulae

Finding Area and Perimeter of a Square or Rectangle

• Area is the measure of the amount of space a shape covers

• Perimeter is the distance all the way around the outside.

length

width

Area of a rectangle = length x width

Perimeter = 2(length and width)

Parallelogram

Length

Perpendicular height

Area of a parallelogram:

length x perpendicular height

Trapezium

Perpendicular height

Length a

Length b

Area of a trapezium:

( length a + length b) x perpendicular height

(a+b) x h

Shape Area PerimeterTriangle ½ (LxW) Add 3 sides

Square LxW 2(L+W)

Rectangle LxW 2(L+W)

Parallelogram L x Height 2(L+W)

Trapezium (A + B) x Height

2

Add all 4 sides

Circle r² x D

To Find Area Complicated Shapes

1. Split them up into basic shapes

2. Work out the area of each bit separately

3. The add them altogether

Perimeters of Complicated Shapes 1. Put a dot in one

corner then go around the shape

2. Write down the length of every side as you go

3. Even sides that have no length given you need to work out

4. Keep going until you get to the dot

Areas and Volumes of 3D Shapes

Volume of a cuboid

• The volume of a 3D shape is a measure of the amount of space it occupies

• Typical units of measure are cubic centimetres (cm³) and cubic metres (m³)

Volume of a Cuboid

• The volume of a cuboid can be written as

length x width x height

= l x w x h

Or you could think of it as the area of the cross section multiplied by the height

Volume of a Prism

• A prism is a 3D shape with the same cross section all along its length

• To calculate the volume of the prism you need to find the area of the cross section and multiply it by the height or length

Volume of prism

= area of cross section x length

Finding the Area of a Prism

This shape is a triangular

The volume is

Area of cross section x length