IGCSE Mathematics: Perimeter and Area Practice Questions
Area measures the space inside a shape and perimeter measures the distance around it. Compound shapes are handled by splitting them into standard shapes and adding or subtracting the areas.
Topic 5.2 of Cambridge IGCSE Mathematics 0580 appears on both papers and inside longer problems. The formula that is misremembered most often is the trapezium, so it is worth writing it out before substituting. The questions below cover the standard shapes and the compound case.
What you need to know for Perimeter and Area
- Rectangle and triangleRectangle area = length x width. Triangle area = half x base x perpendicular height. The height must be perpendicular to the base, not a slanted side.
- Parallelogram and trapeziumParallelogram area = base x perpendicular height. Trapezium area = half x (a + b) x h, where a and b are the parallel sides.
- Compound shapesSplit into standard shapes, or find a larger shape and subtract the missing piece. Show the split clearly on the diagram.
- Perimeter of a compound shapeAdd only the outer edges. Any internal line used to split the shape is not part of the perimeter.
- UnitsPerimeter uses cm or m. Area uses cm2 or m2. Convert all measurements to one unit before calculating.
- Working backwardsIf the area is given and a length is missing, substitute into the formula and solve the resulting equation.
IGCSE Mathematics Perimeter and Area questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
A trapezium has parallel sides of 7 cm and 11 cm, and a perpendicular height of 6 cm. Calculate its area.
Show the worked answer
- Write the formula: area = half x (a + b) x h, where a and b are the parallel sides.
- Add the parallel sides: 7 + 11 = 18.
- Area = half x 18 x 6 = 9 x 6.
- Area = 54 cm2.
A shape consists of a rectangle 12 cm by 8 cm with a semicircle of radius 4 cm attached to one of the shorter sides. Calculate the total area, correct to 3 significant figures.
Show the worked answer
- Split the shape into a rectangle and a semicircle.
- Rectangle area = 12 x 8 = 96 cm2.
- Semicircle area = half x pi x r2 = 0.5 x pi x 42 = 0.5 x pi x 16 = 25.13 cm2.
- Total area = 96 + 25.13 = 121.13, which is 121 cm2 to 3 significant figures.
For the same shape, a rectangle 12 cm by 8 cm with a semicircle of radius 4 cm on one shorter side, calculate the perimeter correct to 3 significant figures.
Show the worked answer
- The 8 cm side where the semicircle is attached is no longer an outer edge, so it is not part of the perimeter.
- The straight outer edges are 12 + 8 + 12 = 32 cm.
- The curved edge is half the circumference of a circle of radius 4: half x 2 x pi x 4 = 4 pi = 12.566 cm.
- Perimeter = 32 + 12.566 = 44.566, which is 44.6 cm to 3 significant figures.
A triangle has an area of 48 cm2 and a base of 12 cm. Calculate its perpendicular height.
Show the worked answer
- Write the formula: area = half x base x height.
- Substitute the known values: 48 = half x 12 x h, which simplifies to 48 = 6h.
- Divide both sides by 6: h = 8.
- The perpendicular height is 8 cm.
Common mistakes in this topic
- Using a slanted side as the height of a triangle or parallelogram.
- Multiplying rather than adding the parallel sides of a trapezium.
- Including internal split lines in a perimeter.
- Mixing units within one calculation.
- Giving an area answer without squared units.
Exam tips
- Write the formula before substituting. It carries a method mark on its own.
- For compound shapes, draw the split line on the diagram and label each part.
- Perimeter counts only the outside. Trace round the shape with a finger to check.
- Convert every measurement to the same unit before you start.
- Check units: cm for perimeter, cm squared for area. Missing the square loses a mark.
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Perimeter and Area FAQs
What is the formula for the area of a trapezium?
Area equals half multiplied by the sum of the two parallel sides, multiplied by the perpendicular height between them. Written as half times (a plus b) times h. The parallel sides are added, never multiplied, and the height must be perpendicular to both.
How do I find the area of a compound shape?
Split it into standard shapes such as rectangles, triangles and semicircles, calculate each area separately, then add them. Alternatively find the area of a larger enclosing shape and subtract the missing piece. Show the split on the diagram so the method is clear.
Does the perimeter include internal lines?
No. The perimeter is the distance around the outside of the finished shape. Any line you draw to split a compound shape into parts is internal and must be excluded, and so must any edge where two parts join together.
What height do I use for a triangle?
The perpendicular height, meaning the distance from the base to the opposite vertex measured at right angles to the base. A slanted side is not the height, even though it is often the length printed on the diagram, which is why questions include both.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.