Area & Perimeter

Spec reference: Geometry and measures - Mensuration
Key idea: Calculate the area and perimeter of 2D shapes including circles and composite shapes.

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Perimeter

Perimeter is the total distance around the outside of a shape.

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Area formulae

Shape	Area
Rectangle	$A=lw$
Triangle	$A={\displaystyle \frac{1}{2}}bh$
Parallelogram	$A=bh$
Trapezium	$A={\displaystyle \frac{1}{2}}(a+b)h$
Circle	$A=\pi r^2$

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Circles

$$\text{Circumference}=\pi d=2\pi r$$$$\text{Area}=\pi r^2$$

Example

Find the area and circumference of a circle with radius 5 cm.

$$A=\pi \times 5^2=25\pi \approx 78.54{\text{ cm}}^2$$$$C=2\pi \times 5=10\pi \approx 31.42\text{ cm}$$

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Sectors and arcs

$$\text{Arc length}=\frac{\theta }{360}\times 2\pi r$$$$\text{Sector area}=\frac{\theta }{360}\times \pi r^2$$

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Composite shapes

Break into simpler shapes, calculate each area separately, then add (or subtract).

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Test Yourself

Question 1 of 5

Area of circle, radius 7 cm (in terms of $\pi$)?