This topic contains material that is usually studied in later years, but continues on from the topics covered previously.
Pythagoras' Theorem
Pythagoras' Theorem is a formula which connects the sides of a rightangled triangle.
In words, it states that if you square the lengths of the two shortest sides of a rightangled triangle and add them together the result is equal to the square of the length of the longest side (the hypotenuse).
A rightangled triangle

Pythagoras' Theorem



Example


Area of Triangles and Quadrilaterals
The area of triangles can be given by a formula:
Area

= 0.5 × base × height
= ^{1}⁄_{2} × b × h
= ^{1}⁄_{2}bh


The formulae for the area of three common quadrilaterals are given below:
Shape

Name 
Area 

Parallelogram 
A = base × height = bh


Rhombus 
A = base × height
= b × h
or
A = ^{1}⁄_{2} × (product of length of diagonals)


Trapezium 
A = ^{1}⁄_{2} × ( a + b ) × h 
Volume of Prisms and Cylinders
A prism is an object that has the same shape (or crosssection) for its whole length.
The volume of the prism equal to the area of the crosssection multiplied by the length.
Below are two common prisms, the triangular prism and the cylinder.
Solid

Name

Volume


Triangular
Prism

V = (shaded area) × l
= ( ^{1}⁄_{2} × b × h ) × l


Cylinder
(circular prism)

V = (shaded area) × h
= ( π r^{2 }) × h
= π r ^{2}h
