Mensuration and calculation: know the formulae: circumference of a circle = 2πr = πd area of a circle = πr² calculate perimeters of 2D shapes, including circles areas of circles and composite shapes

The idea

This row requires you to know the circle formulae and to calculate perimeters and areas, including composite shapes. Circumference = 2πr, which equals πd because the diameter is twice the radius. Area of a circle = πr². To find the perimeter of a composite shape, add every outer edge, using the circumference formula for any circular arc and remembering that a semicircle contributes half the circumference plus its straight diameter. To find the area of a composite shape, split it into rectangles, triangles or circles, calculate each part and add or subtract as appropriate.

For example: A circle of radius 5 cm has area π × 5² = 25π cm², approximately 78.5 cm².

What earns the marks

• Circumference of a circle = 2πr, equivalently πd, using the radius or diameter correctly.
• Area of a circle = πr², squaring the radius before multiplying by π.
• Perimeter of a 2D shape found by adding all outer edges, including curved edges where present.
• Perimeter of a composite shape found by identifying and summing only the boundary edges, not internal dividing lines.
• Area of a composite shape found by splitting it into standard shapes and adding or subtracting their areas.
• Correct use of π, either as an exact value in terms of π or as a decimal approximation as required.

Common mistakes and how to put them right

• Confusing circumference and area formulae.

  Put it right: Circumference uses 2πr or πd, while area uses πr², so check which quantity is asked for.

• Using the diameter in place of the radius in πr².

  Put it right: Halve the diameter first, then square the radius.

• Adding internal dividing lines when finding the perimeter of a composite shape.

  Put it right: Only the outer boundary counts.

• Forgetting the straight edge of a semicircle.

  Put it right: Its perimeter is half the circumference plus the diameter.

Exam tips

• Decide whether the question asks for perimeter, area or volume before choosing a formula.
• Sketch and label the shape, marking radii, diameters and any straight edges you need.
• Leave answers in terms of π when an exact value is requested, and only round at the final step otherwise.
• For composite shapes, write down each part's area or edge length separately so nothing is missed or double-counted.