Area by splitting shapes
Find the area of polygons such as trapezoids, kites, rhombuses, irregular quadrilaterals and other rectilinear or non-rectilinear polygons by decomposition or composition: decompose the shape into rectangles and triangles and add the parts, or compose it into an enclosing rectangle and subtract the pieces outside; record the dimensions used for each piece, check that the pieces neither overlap nor leave gaps, and apply this to real-world problems such as floor plans, gardens and signs, giving answers in square units. The focus is the decomposition and composition strategy, which works for any polygon whether or not a dedicated formula is known
Lesson
Set out your lesson
“Area by splitting shapes means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape or angle name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Area by splitting shapes, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Area by splitting shapes, not mastery.
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Teaching approaches
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1 approach
Area by splitting shapes means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper shapes or a ruler and pencil; Shape or angle name cards. 1. Say the goal of Area by splitting shapes in plain words once. 2. Adult traces or shows one shape/angle and names a key property. 3. Child measures or classifies three shapes/angles and names a property each time. 4. Fresh check: one fresh property name. Record and stop. Done: three correct property names with a sketch or measure. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
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Learning resources
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BBC Bitesize · Practice link — not the full lesson
KS3 Maths
Before you open · source notes
KS3 Maths supports Area by splitting shapes. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Source, access and review notes
Public BBC Bitesize page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
BBC Bitesize. “KS3 Maths.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Find the area of a trapezoid with parallel sides 6 cm and 10 cm and height 4 cm by splitting it into a 6 cm × 4 cm rectangle and two triangles with a combined base of 4 cm (24 + 8 = 32 cm²)
- Find the area of a kite with diagonals 8 cm and 6 cm by enclosing it in an 8 cm × 6 cm rectangle and subtracting the four corner triangles (48 − 24 = 24 cm²)
- Work out the turf needed for a garden shaped like a 12 m × 8 m rectangle with a right triangle (legs 8 m and 3 m) attached to one end (96 + 12 = 108 m²)
“If your child has a plan of a garden shaped like a rectangle with a triangle on one end, could they split it into the rectangle and the triangle, work out each area and add them to find how much turf to buy?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 11–12
Standards