Area of trapezium

Calculate the area of a trapezium using the formula (average of the parallel sides) multiplied by the height, and explain how this formula relates to the area of a rectangle.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM5-3
New NZC (2026)
  • NZC26-P4-MEA-MEA-P-Y9-03
  • NZC26-P3-MEA-MEA-K-Y8-03
  • NZC26-P3-MEA-MEA-P-Y8-04

Resources

Terminology

  • trapezium
  • parallel sides
  • perpendicular height
  • average

Task goals

  • Identify and circle the two parallel sides of a drawn trapezium.
  • Calculate the area of a trapezium from its two parallel sides and perpendicular height, using the formula (average of the parallel sides) times height.
  • Explain why the area formula for a trapezium can be thought of as "the average of the parallel sides multiplied by the height."
  • Work backwards from a given area and one parallel side to find the trapezium's perpendicular height.
  • Find the total area of a composite shape made from a trapezium joined to a rectangle.
  • Substitute a given numeric value of $x$ into algebraic expressions for a trapezium's parallel sides and height, then calculate its area.

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Area of trapezium

Area of trapezium

Do

Finding: the perimeter of 2D shapes; the circumference of circles; the area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle

Statement▸
Year 9 · Measurement · Measuring
NZC26-P4-MEA-MEA-P-Y9-03

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