Angles in triangles (age 11+)
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
Share and support
Teaching Table
Set out your lesson
“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?”
Full guide and materials
- Activity. 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
What to notice. 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
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
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?
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
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.
Learning resources
External links for extra practice. They do not replace Gakuva’s teaching approach.
No additional resources are listed for this topic.
The teaching approach appears above.
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