GCSE Mathematics
GCSE Maths: Geometry & Measures Revision
Geometry, measures and trigonometry revision for GCSE and iGCSE Maths
Geometry is the most visual topic on the paper, and the one where a clear diagram does half the work. Most lost marks come from not identifying which rule applies — an angle fact, a circle theorem, Pythagoras or trigonometry — rather than from the calculation that follows. This free revision engine covers the geometry, measures and trigonometry content of GCSE and International GCSE Maths, with diagrams drawn from the actual numbers in each question. It generates a new question every time and marks your answer as you go.
What the geometry revision engine covers
Foundation and Higher Angles — on a line, in a triangle, between parallel lines, and in polygons Area and perimeter — rectangles, triangles, trapezia and compound shapes Circles — circumference, area, sectors and arc length Volume and surface area — prisms, cylinders, cones and spheres Pythagoras' theorem — finding any side of a right-angled triangle Trigonometry — sine, cosine and tangent, including angles of elevation Transformations — reflections, rotations, translations and enlargements Circle theorems — the angle at the centre, angles in a semicircle, cyclic quadrilaterals Loci and construction — regions defined by a distance Higher tier as well Vectors — column vectors, addition, scalar multiples and magnitude The sine and cosine rules — for any triangle, and the area formula ½ab sin C
Geometry formulas and results you need to know
Angles. Angles on a straight line add to 180°, around a point to 360°, and in a triangle to 180°. The interior angles of an n-sided polygon add to 180(n − 2)°. Pythagoras' theorem. a² + b² = c², where c is the hypotenuse. To find a shorter side, subtract rather than add. Trigonometry. sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. The sine rule. a/sin A = b/sin B = c/sin C. The cosine rule. a² = b² + c² − 2bc cos A. Area of a triangle. ½ab sin C, when you know two sides and the angle between them. Circles. Circumference = 2πr = πd, area = πr². A sector of angle θ has area πr² × θ/360 and arc length 2πr × θ/360. Volumes. Prism = area of cross-section × length. Cylinder = πr²h. Cone = ⅓πr²h. Sphere = ⁴⁄₃πr³. Circle theorems. The angle at the centre is twice the angle at the circumference. The angle in a semicircle is 90°. Opposite angles of a cyclic quadrilateral add to 180°. The angle between a tangent and a chord equals the angle in the alternate segment. Similar shapes. Lengths in the ratio 1 : k give areas 1 : k² and volumes 1 : k³.
How to use it
Choose Foundation or Higher, then pick a topic. Diagrams are generated from the same numbers as the question, so the picture always matches the values you are given. You type your answer and the engine marks it straight away. Signing in saves your accuracy per topic to your GCSE skill tree.
More GCSE Maths revision
Geometry leans on number for its arithmetic and on algebra for rearranging formulae, so it is worth being comfortable with both. Every topic and your progress across all of them is on the revision hub. All of our revision engines are free to use.