Area, surface area and volume

  • Created by: Andrew
  • Created on: 24-10-18 11:49

Area of quadrilaterals

Area of quadrilaterals

For quadrilaterals eg. square or parallelogram, the area can be found with the formula:

Base x Height

Note: The height is the vertical height not the side height in parallelograms

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Area of triangles

Area of triangles

The area of triangles can be found with the formula

1/2 x Base x Height

Again, the height is the vertical height, not the side height (unless the side is vertical).

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Area of trapeziums

Area of trapeziums

The area of trapeziums is a bit harder, the formula is 

1/2 (a+b) x Height

Where 'a' and 'b' are the top and bottom sides

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Area of circles

Area of circles

The area of circles uses a completely different formula to any other

π x r^2

In non-calculator papers, pi will most likely be 3.141

Reminder: 'r^2' means the radius of the circle (the distance from centre to edge) squared 

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Surface area

Surface area

To find the surface area of an object, find the area for each of the sides then add them up

Example: A cube where all the sides are 2cm long

Each side would have an area of 4cm^2  -  2cm x 2cm

A cube has 6 sides, all with the same area

Therefore it becomes 4 x 6 cm^2 -  or 4+4+4+4+4+4 cm^2

Equals 24cm^2


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Volume of cuboids and prisms


The formula for volume in a cuboid is

Base x Height x Length

While in prisms the formula is

Area of cross section x length

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Area of spheres

Area of spheres

Like circles, spheres have a different formula for volume that is 

4/3 x π x r^3


A sphere with a radius of 3cm

4/3 x π x 3^3

4/3 x π x 27

36 x π


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