Area and volume formulae
Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
Lesson
Set out your lesson
“Area and volume formulae 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
- Unit cubes or squared paper nets
- Pencil for recording
Extra for the adult
Worked example. A 2 by 3 by 4 cuboid has volume 24 unit cubes.
Optional challenge. For Area and volume formulae, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Area and volume formulae, not mastery.
Share and support
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Teaching approaches
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1 approach
Area and volume formulae 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: Unit cubes or squared paper nets; Pencil for recording. 1. Say the goal of Area and volume formulae in plain words once. 2. Adult builds a 2×3×4 cuboid and counts 24 unit cubes. 3. Child builds or sketches three cuboids/nets and records length×width×height. 4. Fresh check: one fresh L×W×H volume. Record and stop. Done: three correct volume or net records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceArea and volume formulae practice
Practice key ideas from Area and volume formulae.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Area and volume formulae. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations 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.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Calculate the area of a trapezium using A = ½(a + b) × h and explain why the formula works
- Find the volume of a triangular prism by calculating cross-sectional area × length
- Derive the formula for the volume of a cylinder as π × r² × h by reasoning from the prism formula
“If your child needs to tile a triangular section of a patio with a base of 4 m and height of 3 m, can they work out the area to know how many tiles to buy?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 11–14
Standards