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      Shapes on coordinate grids

      Lesson details

      Learning outcome

      I can calculate perimeter and area of shapes on coordinate grids.

      Key learning points

      1. Shapes on coordinate grids do not often have their measurements clearly written.
      2. Instead, you are expect to calculate the desired lengths.
      3. This may involve Pythagoras' theorem, shape properties or equations of lines for example.

      Keywords

      • Equation of a straight line - An equation of a line is any equation whose graph forms a straight line. These equations can be written in the form y = mx + c.

      Common misconception

      "The graphs of two straight line equations should always intersect at integer points on a coordinate grid."

      The location with which the graphs of two straight line equations intersect can be found by simultaneously solving the pair of equations. The graphs of two straight line equations can intersect at either integer or non-integer values.

      Teacher tip

      For some sets of straight line graphs there may be more than one visible "bounded polygon". Unless explicitly stated to the contrary, always assume the bounded polygon that will be focused on is the one whose sides are made from all the straight lines on the coordinate grid, not a subset of them.

      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.
      Choose the pair of coordinates that is the midpoint of the line segment AB.

      An image in a quiz
      (5, 3)
      Correct answer: (7, 3)
      (7, 7)
      (3, 7)
      4

      Q2.
      The pair of coordinates that is the midpoint of the line segment CD are .

      An image in a quiz
      Correct Answer: (2.5, 9), (2.5,9), (5/2, 9), (5/2,9)

      Q3.
      Which of these calculations finds the gradient of the line segment AB?

      An image in a quiz
      $${4+1}\over{10+5}$$
      $${10+4}\over{5+1}$$
      $${10-4}\over{5-1}$$
      $${5+1}\over{10+4}$$
      Correct answer: $${5-1}\over{10-4}$$

      Q4.
      The gradient of the line segment CD is to 3 decimal places.

      An image in a quiz
      Correct Answer: -0.222

      Q5.
      The length of the hypotenuse of this triangle is cm to 2 decimal places.

      An image in a quiz
      Correct Answer: 26.25, 26.25cm, 26.25 cm

      Q6.
      Find the perimeter of this triangle. Give your answer in metres, correct to the nearest metre.

      An image in a quiz
      Correct Answer: 2 m, 2 metres, 2, 2m

      6 Questions

      Q1.
      To find the length of the line segment CD you need to use theorem.

      An image in a quiz
      Correct Answer: Pythagoras', Pythagoras, Pythagoras's

      Q2.
      The perimeter of trapezium ABCD is units (to 1 decimal place).

      An image in a quiz
      Correct Answer: 31.2, 31.2 units, 31.2units

      Q3.
      Match each measurement to its value.

      An image in a quiz
      Correct Answer:length of line segment EF,7.07 units (2 d.p.)

      7.07 units (2 d.p.)

      Correct Answer:length of line segment FG,15 units

      15 units

      Correct Answer:length of line segment GH,3 units

      3 units

      Correct Answer:length of line segment HI,6.32 units (2 d.p.)

      6.32 units (2 d.p.)

      Correct Answer:length of line segment IE,4 units

      4 units

      Correct Answer:perimeter of pentagon EFGHI,35.4 units (1 d.p.)

      35.4 units (1 d.p.)

      Q4.
      Match each shape to its area.

      An image in a quiz
      Correct Answer:area of rectangle JONM,50 units²

      50 units²

      Correct Answer:area of triangle JMK,10 units²

      10 units²

      Correct Answer:area of triangle KNL,6 units²

      6 units²

      Correct Answer:area of triangle JOL,15 units²

      15 units²

      Correct Answer:area of triangle JKL,19 units²

      19 units²

      Q5.
      The area of triangle QPR is units².

      An image in a quiz
      Correct Answer: 21.5, 21.5 units², 21.5units²

      Q6.
      Calculate the area of the triangle bound by the three straight lines with equations: $$y=2$$, $$y=x$$, $$x+y=12$$. The area is units².

      Correct Answer: 16, 16 units², 16units²

      To help you plan your 10 maths lesson on: Shapes on coordinate grids, download all teaching resources for free and adapt to suit your pupils' needs...