Show WorkingWorked example 1: area of rectangles, triangles and parallelograms
Work out the perimeter of the rectangle.
- The perimeter is the distance all the way round.
- A rectangle has two sides of 7 cm and two of 6 cm.
- 7 + 6 + 7 + 6 = 26 cm.
Answer 26 cm
Geometry and measuresFoundation and Higher
Area and perimeter GCSE questions with answers
8 area and perimeter questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.
Area and perimeter questions cover rectangles, triangles, parallelograms, trapeziums and L-shapes. Perimeter is the distance round the outside, and area is the space inside, measured in square units.
01 / Quiz yourselfTry it, then tap to check
Area and perimeter questions to try
Work each one out on paper first. Then open the answer and compare your working with ours, step by step.
01 / Area of rectangles, triangles and parallelogramsBoth tiers
Work out the area of the rectangle.
Show the answer and working
- Area of a rectangle = length × width.
- 8 × 12 = 96 cm².
Answer 96 cm²
02 / Area of rectangles, triangles and parallelogramsBoth tiers
Work out the area of the rectangle.
Show the answer and working
- Area of a rectangle = length × width.
- 12 × 6 = 72 m².
Answer 72 m²
03 / Area of rectangles, triangles and parallelogramsBoth tiers
Work out the area of the rectangle.
Show the answer and working
- Area of a rectangle = length × width.
- 13 × 5 = 65 m².
Answer 65 m²
04 / Area of a trapeziumBoth tiers
Work out the area of the trapezium.
Show the answer and working
- Area of a trapezium = ½ × (a + b) × h, where a and b are the parallel sides and h is the height between them.
- a + b = 7 + 9 = 16.
- ½ × 16 × 8 = 64 cm².
Answer 64 cm²
05 / Area of a trapeziumBoth tiers
Work out the area of the trapezium.
Show the answer and working
- Area of a trapezium = ½ × (a + b) × h, where a and b are the parallel sides and h is the height between them.
- a + b = 3 + 6 = 9.
- ½ × 9 × 10 = 45 m².
Answer 45 m²
06 / Area of a trapeziumBoth tiers
Work out the area of the trapezium.
Show the answer and working
- Area of a trapezium = ½ × (a + b) × h, where a and b are the parallel sides and h is the height between them.
- a + b = 5 + 10 = 15.
- ½ × 15 × 5 = 37.5 m².
Answer 37.5 m²
07 / Area and perimeter of L-shapesBoth tiers
Work out the area of the shape. All the corners are right angles.
Show the answer and working
- Split the shape into two rectangles. The missing sides are 13 − 6 = 7 m and 10 − 6 = 4 m.
- Left rectangle: 6 × 10 = 60 m². Right rectangle: 7 × 6 = 42 m².
- Total: 60 + 42 = 102 m².
Answer 102 m²
08 / Area and perimeter of L-shapesBoth tiers
Work out the perimeter of the shape. All the corners are right angles.
Show the answer and working
- Find the two missing sides first. Across the top step: 10 − 6 = 4 cm. Down the step: 8 − 4 = 4 cm.
- Add all six sides: 6 + 4 + 4 + 4 + 10 + 8 = 36 cm.
Answer 36 cm
02 / What's covered3 kinds of question
Area and perimeter at GCSE and where marks go
- Area of rectangles, triangles and parallelogramsBoth tiers
- Area of a trapeziumBoth tiers
- Area and perimeter of L-shapesBoth tiers
Worked example 2: area and perimeter of l-shapes
Work out the perimeter of the shape. All the corners are right angles.
- Find the two missing sides first. Across the top step: 10 − 8 = 2 cm. Down the step: 13 − 3 = 10 cm.
- Add all six sides: 8 + 10 + 2 + 3 + 10 + 13 = 46 cm.
Answer 46 cm
A common mistake
Using the sloping side instead of the height. The area of a triangle is ½ × base × height, where the height is at right angles to the base, so a base of 10 cm and a height of 6 cm give 30 cm².
03 / Practise itiPhone and iPad
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