Geometry and Mensuration

Angles

Angles on a straight line sum to 180°; angles at a point sum to 360°; angles in a triangle sum to 180°; the sum of interior angles of a polygon with $n$ sides is $(n-2)\times 180°$.

Pythagoras' theorem

In a right triangle, $a^2+b^2=c^2$, where $c$ is the hypotenuse (the longest side, opposite the right angle).

Circle theorems

Key ones JAMB tests: the angle at the centre is twice the angle at the circumference standing on the same arc; angles in the same segment are equal; the angle in a semicircle is 90°; opposite angles of a cyclic quadrilateral sum to 180°.

Perimeter and area

• Rectangle: perimeter $=2(l+w)$, area $=l\times w$.
• Triangle: area $=\frac{1}{2}\times \text{base}\times \text{height}$.
• Circle: circumference $=2\pi r$, area $=\pi r^2$.
• Trapezium: area $=\frac{1}{2}(a+b)h$, where $a,b$ are the parallel sides.

Volume and surface area of solids

• Cuboid: volume $=l\times w\times h$.
• Cylinder: volume $=\pi r^{2}h$, curved surface area $=2\pi rh$.
• Cone: volume $=\frac{1}{3}\pi r^{2}h$.
• Sphere: volume $=\frac{4}{3}\pi r^3$, surface area $=4\pi r^2$.