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8.2 Trapezia and Changing Units

GCSE Maths Foundation · Edexcel · Chapter 8: Perimeter, Area, and Volume 1

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: converting units of length and area, and the area of a trapezium. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Convert between mm, cm, m and km
  • Convert between units of area: mm², cm² and m²
  • Use the formula for the area of a trapezium
  • Solve problems with trapezia, including mixed units and missing lengths

Key words

  • Trapezium: A four-sided shape with exactly one pair of parallel sides. Plural: trapezia.
  • Parallel sides: Sides that point in the same direction and never meet. In the formula they are a and b.
  • Square unit: A unit of area, such as 1 cm²: the area of a square with sides of 1 cm.
  • Convert: Change a measurement to a different unit without changing its size.

Converting lengths

  • cm; To mm; Do this × 10
  • m; To cm; Do this × 100
  • km; To m; Do this × 1000
  • mm; To cm; Do this ÷ 10
  • cm; To m; Do this ÷ 100
  • m; To km; Do this ÷ 1000

Worked example: lengths

(a) 3.6 m = 3.6 × 100 = 360 cm
(b) 4500 m = 4500 ÷ 1000 = 4.5 km
(c) 82 mm = 82 ÷ 10 = 8.2 cm

Answer: 360 cm, 4.5 km, 8.2 cm

Key fact: Changing to a smaller unit gives a bigger number (multiply). Changing to a bigger unit gives a smaller number (divide).

Converting areas

A square 1 cm by 1 cm is also 10 mm by 10 mm, so its area is 10 × 10 = 100 mm². Square the length conversion!

  • cm² → mm²; Conversion × 100 (10 × 10)
  • m² → cm²; Conversion × 10 000 (100 × 100)
  • mm² → cm², cm² → m²; Conversion ÷ 100, ÷ 10 000

Worked example: areas

(a) 6 m² = 6 × 10 000 = 60 000 cm²
(b) 350 mm² = 350 ÷ 100 = 3.5 cm²

Answer: 60 000 cm² and 3.5 cm²

Area of a trapezium

Two identical trapezia fit together to make a parallelogram with base (a + b) and height h. So one trapezium is half of that.

Key fact: Area of a trapezium = 1/2 × (a + b) × h, where a and b are the parallel sides and h is the perpendicular height

Worked example: using the formula

A = 1/2 × (6 + 10) × 5 = 1/2 × 16 × 5 = 8 × 5 = 40

Answer: 40 cm²

Trapezium problems

Worked example: mixed units

A trapezium has parallel sides 80 cm and 1.2 m, and height 50 cm. Find its area in m².
Change everything to metres first: 0.8 m, 1.2 m, 0.5 m.
A = 1/2 × (0.8 + 1.2) × 0.5 = 1/2 × 2 × 0.5 = 0.5

Answer: 0.5 m²

Worked example: finding the height

A trapezium has area 63 cm² and parallel sides 8 cm and 10 cm. Find its height.
1/2 × (8 + 10) × h = 63, so 9h = 63 and h = 7.

Answer: 7 cm

The perimeter of a trapezium is just the sum of its four sides. The height is not a side, so do not add it.

Common mistakes

  • Using × 100 to change m² to cm². It is × 10 000, because 100 × 100 = 10 000.
  • Using a sloping side instead of the perpendicular height in the trapezium formula.
  • Forgetting to halve, or halving only one of the parallel sides.
  • Using different units in the same formula (for example cm and m together).

Revision questions

Try these, then check your answers below each one.

Question 1. Convert 3.5 m to centimetres.

Answer: 350 cm

Working: 3.5 × 100 = 350 cm.

Question 2. Convert 4 cm² to mm².

Answer: 400 mm²

Working: 4 × 100 = 400 mm².

Question 3. A trapezium has parallel sides of 5 cm and 9 cm, and a perpendicular height of 4 cm. Work out its area.

Answer: 28 cm²

Working: 1/2 × (5 + 9) × 4 = 7 × 4 = 28 cm².

Related lessons

Continue in the full course

This lesson is section 8.2 (EGCMF0802) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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