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      Lesson details

      Learning outcome

      I can derive the formula for the area of a triangle.

      Key learning points

      1. It is possible to find a relationship between triangles and parallelograms.
      2. You can use this relationship to find a formula for the area of a triangle.
      3. It is possible to identify the base and perpendicular height of any triangle even when they are not obvious.
      4. The formula can be used to find the area of any triangle.

      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 forget to halve after multiplying the base and the perpendicular height.

      The area of a triangle is equal to half the area of the parallelogram formed by two of those triangles.

      Teacher tip

      Ensure pupils have the opportunity to cut out and physically mainpulate the trianges to form different quadrilaterals and have them discuss as a class which quadrilateral they could all make.

      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.
      What type of shape is this?

      An image in a quiz
      equilateral triangle
      isosceles triangle
      Correct answer: right-angle triangle
      scalene triangle

      Q2.
      What type of shape is this?

      An image in a quiz
      Correct answer: equilateral triangle
      isosceles triangle
      right-angle triangle
      scalene triangle

      Q3.
      What type of shape is this?

      An image in a quiz
      equilateral triangle
      isosceles triangle
      right-angle triangle
      Correct answer: scalene triangle

      Q4.
      What type of shape is this?

      An image in a quiz
      equilateral triangle
      Correct answer: isosceles triangle
      right-angle triangle
      scalene triangle

      Q5.
      True or false? In order to calculate the area of a shape, you sum the side lengths of the shape.

      True
      Correct answer: False

      Q6.
      The angles in a triangle sum to

      Correct Answer: 180 degrees, 180

      6 Questions

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

      Correct Answer: base

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

      An image in a quiz
      True
      Correct answer: False

      Q3.
      True or false? You 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 8 cm and a perpendicular height of 5 cm (you do not need to give the units).

      Correct Answer: 20, Twenty

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

      Correct Answer: parallelogram

      Q6.
      Which of these is not a way to calculate the area of this triangle?

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

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