Area of Triangle

WALT (We Are Learning To)

• Calculate the area of any triangle using the formula:
  Area = ½ × base × perpendicular height
• Identify the base and the perpendicular height of triangles even when heights are not on the base line.
• Apply understanding of area calculation to a variety of triangle problems.

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National Curriculum References

• Mathematics KS2, Year 6:
  • Geometry - properties of shapes (6.3.26): “Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.”
  • Measurement: “Calculate and compare the area of rectangles (including squares) and estimate the area of irregular shapes."
• Statutory Framework:
  • Develop fluency in using the formula for the area of triangles and interpret geometric problems involving triangles (DfE Mathematics Programmes of Study for Key Stage 2).

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Success Criteria

• I can identify the base and perpendicular height of any triangle.
• I can use the area formula correctly to find the area of triangles.
• I can solve problems involving different dimensions and units, including converting where necessary.
• I can explain why the perpendicular height must form a right angle with the base.

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Resources

• Whiteboard and markers or digital presentation
• Printed worksheet (based on the file content with diagrams measuring triangles and grids)
• Rulers and set squares (to measure and identify heights)
• Calculators (optional, for differentiation)
• Interactive geometry app (e.g., Geogebra on tablets or computers)
• Prepared triangles on squared paper for visual aid

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Lesson Structure (60 minutes)

Introduction (10 minutes)

• Engage & Review: Display a right-angled triangle on the board with base and height marked, demonstrate the area formula.
• Ask pupils: “What parts of the triangle do you need to know to work out the area?”
• Recap prior learning: area of rectangles and squares, emphasizing the couple between bases and heights.
• Introduce the WALT and success criteria on the board.

Whole Class Teaching (15 minutes)

• Use slides/presentation from Area of any triangle 1003.pptx:
  • Show images with measurements; discuss which side is the base and which is the perpendicular height.
  • Challenge pupils to identify the base and height on diagrams where the height is inside the triangle but not a side length (height shown with right angle marker).
  • Demonstrate how to draw and measure the perpendicular height if not given, using set squares or on paper.
  • Work through 2-3 examples from the presentation, calculating areas out loud, showing all steps and units of measurement.
• Emphasise: the perpendicular height is always measured at a 90° angle to the base.

Guided Practice (15 minutes)

• Provide pupils with worksheet (designed from the presentation’s questions): different triangles with various bases and perpendicular heights.
• Pupils will:
  • Identify and label base and perpendicular height.
  • Calculate the area of each triangle.
• Round-robin: teacher circulates, scaffolding for pupils who struggle using rulers and protractors to identify perpendicular heights.
• Use questioning: “Why can’t we use a side that isn’t perpendicular as height?” “What units do we use for area?”

Differentiation

• Support: Use triangles drawn on 1cm² grid paper to count squares as aid in understanding area. Use calculators for multiplication. One-to-one or small group support with physical set squares.
• Mainstream: Workbook questions with varying difficulty, some requiring students to draw heights.
• Extension: Provide irregular triangles where the perpendicular height must be drawn outside the triangle (obtuse triangles). Include some problem-solving questions such as:
  • “A triangle has an area of 33 cm² and a base of 6 cm. What is the perpendicular height?”
  • Explore area conversion between cm² and m² where dimensions are mixed (e.g., base in metres, height in centimetres).

Plenary (10 minutes)

• Invite students to share their answers and methods for one or two chosen problems.
• Use a quick quiz game: display triangle images asking teams to point out the base and height, then calculate area mentally or in pairs.
• Recap the WALT and success criteria by asking students to self-assess (thumbs up/down) whether they achieved each one today.
• Highlight common misconceptions (e.g., confusing side length and perpendicular height) and address these explicitly.

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Assessment

• Informal formative assessment during guided practice through questioning and observations.
• Collect worksheets to review accuracy and understanding.
• Use plenary quiz responses to gauge class-wide misconceptions.
• Optional exit ticket: Pupils write a sentence explaining how to find the area of a triangle and one thing they found tricky.

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Homework / Extension Activity

• Create a “triangle area hunt”: pupils find 3 real-life triangular objects at home, measure base and height (approximately), and calculate area.
• Challenge: Draw two different triangles with the same base and height and calculate their areas to verify if the area changes.

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Reflection on Teaching and Learning

• Note which pupils could confidently find perpendicular heights without help.
• Adapt next lesson to revisit units or right angle concepts if many found drawing perpendicular heights challenging.
• Consider technology integration by encouraging pupils to use geometry software to manipulate triangles for deeper conceptual understanding next lesson.

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By clearly aligning with the National Curriculum, incorporating visual aids, interactive activities, and differentiated challenges, this lesson plan aims to ensure every Year 6 pupil in England develops a confident and thorough understanding of how to find the area of any triangle. The use of grids and real-life connections aims to ‘wow’ any teacher adopting this resource!