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GCSE Maths / Edexcel

Perimeter and area of 2D shapes

Choose the correct perimeter or area method for rectangles, triangles, parallelograms and trapezia, using perpendicular height and correct units.

Geometry and MeasuresFoundation and HigherGrades 2 to 5Skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Perimeter and area

Pearson Edexcel GCSE Maths geometry G9: identify and apply formulae for perimeter and area of triangles, quadrilaterals and compound 2D shapes.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Perimeter is the distance around the outside of a shape. Add all the side lengths.

Area is the space inside a shape. Area uses square units such as cm² or m².

For a rectangle, area = base x height.

For a triangle, area = 1/2 x base x height. The height must be perpendicular to the base.

For a parallelogram, area = base x height. Do not use the slanted side as the height.

For a trapezium, area = 1/2 x (sum of parallel sides) x height.

If the question says fencing, border or edge, it usually means perimeter. If it says cover, paint, grass or floor, it usually means area.

If a diagram is not drawn accurately, trust the written measurements, not what the shape looks like.

When units are mixed, convert them before calculating. Do not multiply centimetres by metres.

Key rulePerimeter is around the edge. Area is inside the shape. Area formulae use perpendicular height.

Diagram guide

baseheightheightbasearea = base x heightarea = 1/2 x base x height
Base and perpendicular heightArea formulae use the perpendicular height. A slanted side is not the height unless it meets the base at 90 degrees.
heightbaseparallelogram: base x heightheightabtrapezium: 1/2 x (a + b) x height
Parallelogram and trapeziumThese questions test whether you can identify the base, parallel sides and perpendicular height.
area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
Perimeter, area and unitsPerimeter is one-dimensional, so use cm or m. Area is two-dimensional, so use cm² or m².

Worked examples

Rectangle

Find the area of a rectangle with length 8 cm and width 5 cm.

area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
Example: rectangle areaArea means the space inside the rectangle.
  1. Area = length x width.
  2. 8 x 5 = 40.

Answer: 40 cm²

Triangle

Find the area of a triangle with base 12 cm and height 7 cm.

baseheightheightbasearea = base x heightarea = 1/2 x base x height
Example: triangle areaThe 7 cm height must be perpendicular to the 12 cm base.
  1. Area = 1/2 x base x height.
  2. 1/2 x 12 x 7 = 42.

Answer: 42 cm²

Perimeter

A rectangle is 9 cm by 4 cm. Find its perimeter.

area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
Example: perimeterPerimeter means the distance around all four sides.
  1. Perimeter = 9 + 4 + 9 + 4.
  2. Perimeter = 26.

Answer: 26 cm

Trapezium area

A trapezium has parallel sides 6 cm and 10 cm, with perpendicular height 5 cm. Find its area.

heightbaseparallelogram: base x heightheightabtrapezium: 1/2 x (a + b) x height
Example: trapezium areaAdd the two parallel sides first, then multiply by the height and halve.
  1. Area = 1/2 x (a + b) x h.
  2. Area = 1/2 x (6 + 10) x 5.
  3. Area = 1/2 x 16 x 5 = 40.

Answer: 40 cm²

Common mistakes

  • Using area when the question asks for perimeter.
  • Forgetting to halve when finding the area of a triangle.
  • Using a slanted side instead of the perpendicular height.
  • Writing cm instead of cm² for area.
  • Adding the parallel sides of a trapezium but forgetting to halve.
  • Converting units after calculating instead of before calculating.

Quick exercise

Try these before moving to the exam-style questions.

  1. Find the area of a rectangle 6 cm by 11 cm.
    area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
    Quick check: rectangle areaMultiply length by width.
  2. Find the perimeter of a rectangle 7 m by 3 m.
    area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
    Quick check: perimeterAdd all four sides around the outside.
  3. Find the area of a triangle with base 10 cm and height 9 cm.
    baseheightheightbasearea = base x heightarea = 1/2 x base x height
    Quick check: triangle areaUse half times base times perpendicular height.
  4. Find the area of a parallelogram with base 8 cm and height 6 cm.
    heightbaseparallelogram: base x heightheightabtrapezium: 1/2 x (a + b) x height
    Quick check: parallelogramUse base times perpendicular height.
  5. Find the area of a trapezium with parallel sides 5 cm and 9 cm, height 4 cm.
    heightbaseparallelogram: base x heightheightabtrapezium: 1/2 x (a + b) x height
    Quick check: trapeziumAdd the parallel sides, multiply by height, then halve.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

A rectangle has length 12 cm and width 7 cm. Work out its area.

area insideperimeter is around the outsideperimeter uses cm or marea uses cm² or m²
Question diagram: rectangle areaThe question asks for area, so multiply the two side lengths.
arearectanglefoundation geometry
Standard exam styleFoundation and HigherCalculator3 marks

A triangle has base 13 cm and perpendicular height 8 cm. Work out its area.

baseheightheightbasearea = base x heightarea = 1/2 x base x height
Question diagram: triangle areaPerpendicular height is the height used in the formula.
triangle areaperpendicular heightmethod marks
ChallengeFoundation and HigherEither4 marks

A trapezium has parallel sides 6 cm and 14 cm. Its height is 9 cm. Work out its area.

heightbaseparallelogram: base x heightheightabtrapezium: 1/2 x (a + b) x height
Question diagram: trapezium areaUse the two parallel sides and the perpendicular height.
trapezium areacompound methodgeometry reasoning