Mathematics·Geometry·procedural
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
Suggested ages 11–14
Evidence of 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
Assessment prompt
If Angles in triangles (age 11+) 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?
Standards alignment
7.G.6US · ccss-math
Solve real-world and mathematical problems involving area, volume and surface area
Common Core State Standards for Mathematics · 7
8.G.9US · ccss-math
Volumes of cones, cylinders, and spheres
Common Core State Standards for Mathematics · 8
KS3.Maths.Geo.1GB · uk-nc-2013
Perimeter, Area and Volume Formulae
The national curriculum in England: Key stages 1 and 2 framework document · Key Stage 3