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      Using the formula for the area of a triangle

      Lesson details

      Learning outcome

      I can use the formula for the area of a triangle to calculate missing side lengths.

      Key learning points

      1. 0.5 x base x perpendicular height can be used to find the area of any triangle.
      2. Missing sides can be found if the area is known.

      Keywords

      • Base - The base is the side which is perpendicular to the height.

      • Perpendicular height - The perpendicular height is the perpendicular distance from the base to the opposite vertex.

      Common misconception

      Pupils may think the height of the triangle is the slanted height rather than perpendicular.

      The base and height to be used must be perpendicular (at a right angle) to each other.

      Teacher tip

      If pupils are not ready to use algebra within this topic, use the correct mathematical terms for the unknown sides alongside the algebra to support their understanding of what the letter represents.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      The perpendicular is the perpendicular distance from the base to the opposite vertex.

      Correct Answer: height

      Q2.
      True or false? You can calculate the area of this triangle.

      An image in a quiz
      Correct answer: True
      False

      Q3.
      True or false? We can calculate the area of this triangle.

      An image in a quiz
      True
      Correct answer: False

      Q4.
      Calculate the area of a triangle with a base of 13 cm and a perpendicular height of 3 cm (you do not need to give the units).

      Correct Answer: 19.5 cm$$^2$$, 19.5

      Q5.
      Two triangles can always be placed together to create a parallelogram.

      Correct Answer: identical, congruent

      Q6.
      Which of these is the correct way to calculate the area of this triangle?

      An image in a quiz
      base $$\times$$ perpendicular height $$\times$$ 0.2
      base $$\times$$ perpendicular height $$\div {1 \over 2}$$
      Correct answer: $$b \times h \times {1 \over 2}$$
      $$bh \times 2$$

      6 Questions

      Q1.
      The base and height of this triangle measure:

      An image in a quiz
      13.3 mm and 15.3 mm
      Correct answer: 18.3 mm and 15.3 mm
      13.3 mm and 18.3 mm
      13.3 mm and 19.3 mm

      Q2.
      Select the correct expression for the area of the triangle.

      An image in a quiz
      Correct answer: $$ac \over 2$$
      $$ab \over 2$$
      $$bc \over 2$$

      Q3.
      Select the correct expression for the area of the triangle.

      An image in a quiz
      $$28bd \over 2$$
      $$20bd^{2}t \over 2$$
      Correct answer: $$35dt \over 2$$

      Q4.
      Calculate the missing side length.

      An image in a quiz
      Correct Answer: 10 cm, 10

      Q5.
      Calculate the missing side length.

      An image in a quiz
      Correct Answer: 3.3 cm, 3.3

      Q6.
      Calculate the missing side length.

      An image in a quiz
      Correct Answer: 2.5 cm, 2.5

      To help you plan your 7 maths lesson on: Using the formula for the area of a triangle, download all teaching resources for free and adapt to suit your pupils' needs...