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Area of a trapezoid, step by step

A trapezoid has two parallel sides of different lengths, so its area averages them and multiplies by the height.

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The question
434 cm²

Area of a trapezium, 3 and 4 by 4

4 cm 3 cm 4
  1. A trapezium. Two of its numbers matter and they are not the two longest lines — find them before working anything out.
  2. The two PARALLEL sides are 3 cm and 4 cm. They are the pair that counts.
  3. The height is the DASHED line — straight up from the base, at a right angle to it: 4 cm. It is not the sloping side, even though the sloping side is longer and is written right next to it.
  4. Average the two parallel sides: (3 + 4) ÷ 2 = 3.5. That is the width of the rectangle this trapezium is worth.
  5. Then it is that width times the height: 3.5 × 4 = 14 square cm.

How it works.

  1. 01

    A trapezium. Two of its numbers matter and they are not the two longest lines — find them before working anything out.

  2. 02

    The two PARALLEL sides are 3 cm and 4 cm. They are the pair that counts.

  3. 03

    The height is the DASHED line — straight up from the base, at a right angle to it: 4 cm. It is not the sloping side, even though the sloping side is longer and is written right next to it.

  4. 04

    Average the two parallel sides: (3 + 4) ÷ 2 = 3.5. That is the width of the rectangle this trapezium is worth.

  5. 05

    Then it is that width times the height: 3.5 × 4 = 14 square cm.

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