Geometry & Measures is a core part of GCSE Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.
Key concepts
Angle rulesAngles on a line, around a point, in triangles and parallel lines.
PolygonsInterior and exterior angles of polygons.
Circle theoremsAngle and chord properties of circles.
TransformationsTranslation, reflection, rotation and enlargement.
Congruence & similarityIdentical shapes versus same shape, different size.
ConstructionsAccurate drawings using compasses and a ruler.
PerimeterDistance around a 2-D shape.
AreaSpace inside a 2-D shape (e.g. triangle = ½bh, circle = πr²).
VolumeSpace inside a 3-D solid (cubic units).
Surface areaTotal area of all faces of a solid.
CirclesCircumference = 2πr; area = πr².
UnitsLength (cm), area (cm²), volume (cm³).
TranslationSlide a shape without rotating or reflecting; described by a vector.
ReflectionFlip across a mirror line; the image is the same distance behind the line.
Common mistakes to avoid
Questions where students often pick the tempting wrong answer — make sure you know the right one:
What is the formula for the area of a circle?✗ The area of a circle is 2 * pi * r — the same as the circumference formula. ✓ pi * r^2 (pi times the radius squared).
In Pythagoras' theorem, which side does c^2 represent?✗ c^2 represents any side of the triangle as long as the other two are squared. ✓ The hypotenuse — the longest side, opposite the right angle.
What is the relationship between the angle at the centre and the angle at the circumference subtended by the same arc?✗ The angles are equal because they are subtended by the same arc. ✓ The angle at the centre is twice the angle at the circumference.
What is the sum of the interior angles of any pentagon?✗ 360 degrees, because all polygons' angles sum to one full turn. ✓ 540 degrees — use (n - 2) x 180 with n = 5.
What is the difference between area and perimeter?✗ Area and perimeter are different names for the same measurement. ✓ Perimeter is the total distance around the outside; area is the amount of surface inside (measured in square units).
Practise Geometry & Measures — free games
Test yourself with these quick revision games for this topic:
See all 17 games in the Subjects Arcade →
More GCSE Maths topics
← All revision guides
Want to revise every topic this smart?
The Velvet Method teaches you to use AI to revise any subject — £25, lifetime access.
Explore the Course →