Playbook
Mensuration 2D
197 q · 23% HARD · about 9.4 a paper. Wheels, arcs and re-bent wires are nearly free; touching circles (62% HARD) and shaded regions (40%) are where the wrong answers come from. Attempt those two only on a clean solve.
- Questions in the bank
- 197
- q/paper (21 papers)
- 9.38
- Tagged HARD
- 23%
- Subtopics
- 8
Strand: Cornerstone
When you’ll see it
Area or perimeter of a plane figure, a wheel's revolutions, or a shaded region between shapes.
How this chapter is tested
197 questions, steady at about 9.4 a paper. Most of it is formula application: triangle areas, quadrilaterals, circles and sectors. Wheels, arcs and re-bent wires are nearly free (4-6% HARD).
The HARD sits in three pages: touching circles (13 questions, 62% HARD), combined and shaded regions (40%) and inscribed figures (34%). These are set-up problems — the formula is easy once you see which shapes make up the region.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Triangles and quadrilaterals
Heron's formula, the equilateral √3/4 a², rhombus and trapezium areas.
Circles, arcs and sectors
Sector = θ/360 × πr², arc = θ/360 × 2πr.
Wheels and rings
Revolutions = distance ÷ circumference.
Inscribed and circumscribed figures
A square in a circle has diagonal = diameter; a circle in a triangle has r = area ÷ semi-perimeter.
Shaded regions
The shaded area is a whole minus the pieces; touching circles give a triangle minus three sectors.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Diameter for radius
A 14 cm diameter circle used as r = 14.
The gap between three circles
The three 60° sectors add to half a circle, not a whole one.
Perimeter of a sector
Arc length plus TWO radii.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Mensuration 2D notesDrill every Mensuration 2D question
197 questions from the bank, across 8 subtopics.
Drill one subtopic at a time
The 8 subtopics, in teaching order.
- Arcs, Sectors and SegmentsDrill Arcs, Sectors and Segments
- Circumference, Wheels and RingsDrill Circumference, Wheels and Rings
- Equal Perimeters and Re-bent WiresDrill Equal Perimeters and Re-bent Wires
- Areas of TrianglesDrill Areas of Triangles
- Rectangles, Squares and Other QuadrilateralsDrill Rectangles, Squares and Other Quadrilaterals
- Inscribed and Circumscribed FiguresDrill Inscribed and Circumscribed Figures
- Combined and Shaded RegionsDrill Combined and Shaded Regions
- Touching CirclesDrill Touching Circles
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