2D Shape Area Formulas

You'll need to memorise these area formulas for your exams, and they're actually quite straightforward once you understand the patterns. Each shape has its own special formula that relates to its unique properties.

For circles, the area is π × radius², whilst a sector (like a slice of pizza) uses the fraction θ/360 × π × radius². The arc length follows a similar pattern: θ/360 × π × diameter.

Quadrilaterals are much simpler - squares and rectangles both use base × height. A trapezium (with two parallel sides) uses ½$a+b$ × height, where 'a' and 'b' are the lengths of the parallel sides.

Top Tip: Always write down the formula first, then substitute your values - this prevents silly mistakes and shows your working clearly.

Compound Shapes Made Easy

Compound shapes look intimidating, but they're just regular shapes stuck together. The trick is splitting them into recognisable parts like rectangles and triangles.

In the example shown, a 6×4 rectangle (24 cm²) combines with a 3×6 rectangle (9 cm²) to give 33 cm² total. Always label each section clearly and work methodically through each part.

Complex Compound Shapes

More challenging compound shapes require you to identify multiple sections - rectangles, trapeziums, or triangles all joined together. Don't panic when you see these; just break them down systematically.

The example demonstrates splitting a complex shape into two rectangles $each 9×20 = 180 cm²$ and one trapezium using ½(20+15) × 14 = 245 cm². Notice how labelling sections A, B, and C keeps everything organised.

Remember: Draw clear lines to separate each section and double-check your measurements before calculating.

Estimation Through Rounding

Estimation saves you time and helps check if your calculator answers make sense. Round numbers to the nearest thousand or hundred to make mental maths easier.

For 9268 × 3672, round to 9000 × 4000 = 36,000,000. Since 9268 is below 9500, it rounds down, whilst 3672 rounds up because it exceeds 3500.

This technique is brilliant for spotting calculator errors and getting quick approximations during exams when time is tight.