# Areas

Sorry! It’s another page of tedious formulae.

Area Of A Triangle Half the base times the height.

0.5 x h x b

Area Of A Parallelogram Base times the height.

b x h

Area Of A Trapezium Average of the parallel sides times the distance between them.

0.5(a+b) x h

Composite Shapes

In exams some shapes will be a mix of shapes you know the area formula for. If you need to find the area just split it into its separate parts and add their areas together. For example the shape below you can split into a square and a triangle. Area Of A Circle The area equals pi times the radius squared.

Circumference is pi times the diameter, or, twice the radius.

Area = πr2

Circumference = πD = 2πr

Area Of A Sector Area of sector = y/360 x area of whole circle
Length of minor arc = y/360 x circumference of whole circle

Area Of A Segment

A segment is the bitt left over when you draw a triangle in a circle using its radius as two sides. Sounds complicated…but it’s just the bit marked with lines in the diagram below….see…not so bad. But how would you work out its area?

First you find the area of the sector, then subtract the area of the triangle.

Area of sector = 93/360 x π x 3.5= 9.941831…

Area of triangle = 0.5rsinx = 0.5 x 3.5sin 93 = 6.116606…

NOTE: You might want to refresh with the notes on the sine rule if you’re not sure where we got this formula from

So area = 9.941831…- 6.116606… = 3.83 (2 d.p.)