4.9aFoundation tier4MA1 · Section 4: Geometry and trigonometry

Area & perimeter (2D shapes, circles)

Key learnings

Standard area & circle formulae
Rectangle $bh$ ; triangle $\tfrac12 bh$ ; trapezium $\tfrac12(a+b)h$ ; circle area $\pi r^2$ ; circumference $\pi d = 2\pi r$ .
Compound shapes: split into parts
Break the shape into rectangles/triangles/trapezia, work out each, then add (or subtract a hole).

Drawn from real examiner reports.

Treating a compound shape as a single shape

Applying one formula to the whole figure instead of splitting it into a rectangle plus a trapezium (etc.).

Forgetting to add a part back in

Finding each piece correctly but omitting one when combining (e.g. not adding a height back on).

Mixing up area and circumference

Using $2\pi r$ when area $\pi r^2$ is needed (or vice versa).

For a segment: sector minus triangle
Segment area $=$ sector area $-$ triangle area $= \tfrac{\theta}{360}\pi r^2 - \tfrac12 r^2\sin\theta$ .

Circle circumference $= \pi d = 2\pi r$ . Don't confuse area ( $\pi r^2$ ) with circumference ( $2\pi r$ ).

Foundation

Area of a circle?

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Question 1 of 1Foundation2 marks

Find the area of a circle of radius $7$ cm, correct to 1 d.p. (use $\pi = 3.14159\ldots$ ).

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