Topic 3 of 4Pearson EdExcel

Geometry & Mensuration

Area, volume, angles, and geometric properties

Angles:

Angles on a straight line = 180°

Angles in a triangle = 180°

Angles in a quadrilateral = 360°

Vertically opposite angles are equal

Corresponding angles (parallel lines) are equal (F-angles)

Alternate angles (parallel lines) are equal (Z-angles)

2D Shapes — Area formulae:

Rectangle: A = l × w

Triangle: A = ½bh

Circle: A = πr², Circumference = 2πr

Trapezium: A = ½(a + b)h

3D Shapes — Volume formulae:

Cuboid: V = l × w × h

Cylinder: V = πr²h

Cone: V = ⅓πr²h

Sphere: V = ⁴⁄₃πr³

Surface area: Sum of area of all faces.

Pythagoras' theorem: a² + b² = c² (right-angled triangles, c = hypotenuse)

Trigonometry (SOHCAHTOA):

sin θ = Opposite/Hypotenuse

cos θ = Adjacent/Hypotenuse

tan θ = Opposite/Adjacent

Key Points to Remember

1Triangle area = ½bh; Circle area = πr²; Cylinder volume = πr²h
2Pythagoras: a² + b² = c²
3SOHCAHTOA for trigonometry in right triangles
4Corresponding and alternate angles are equal in parallel lines

Pakistan Example

The Minar-e-Pakistan — Geometry in Lahore's Architecture

The Minar-e-Pakistan tower is approximately 60m tall. Standing 80m away, the angle of elevation to the top can be found: tan θ = 60/80 = 0.75 → θ = 36.9°. The circular base has radius 15m → area = π × 15² ≈ 707 m². Pakistan's construction boom (CPEC infrastructure) constantly requires trigonometry and mensuration calculations on site.

Quick Revision Infographic

Mathematics — Quick Revision