Area of Circles and Composite Shapes

Key Facts and Exam Tips

• The area of a circle is found using the formula A = r². You square the radius first and then multiply by . Make sure you know how to do this on your own calculator.
  
• When calculating with this formula, remember to check that you have used the radius (not the diameter) in your calculation. The radius is half the diameter.
  
• The value of to use will depend on the question. The value is often given in the question, and if this is the case you should use that value. If you only need an approximate answer (eg for a mental test) you could use = 3 or = 22/7. If you are using a scientific calculator the button can be used.
  
• Only round your answer at the end of the final calculation, giving the degree of accuracy required in the question. If you are not told the degree of accuracy to use then three significant figures is often appropriate.
  
• Remember that to find the area of a semi-circle you can find the area of the whole circle using A = r² and then halve it. Similarly, for a quarter circle (quadrant) you divide the area of the whole circle by four.
  
• Composite shapes are made up of simpler shapes put together. To find their area you will need to identify the simpler shapes, like rectangles, squares, triangles and circles, or parts of circles.
  
• You should divide the shape up using lines on the diagram given in the question, so that each shape's area is clear. Also mark any extra dimensions (lengths) that you need to use to find these areas.
  
• Calculate the area of each part you have identified and then find the total area by adding them together. In some questions a shape may have 'holes' instead and you will need to subtract in this case.
  
• If lengths are given in centimetres, the area will be in square centimetres; for metres in square metres; for feet in square feet and so on. The question will tell you what units to state your answer in and you may have to convert between units. When changing cm² to m² remember that there are 10 000cm² to 1m². Alternatively, convert the lengths to metres before finding the area.
  
• Remember that you get marks for your method, even if the final answer is wrong. Your working should include a calculation for the area of each part of the composite shape and show how you combined these to get the total area.