## More Measurement

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 right-angled triangle.

In words, it states that if you square the lengths of the two shortest sides of a right-angled triangle and add them together the result is equal to the square of the length of the longest side (the hypotenuse).

 A right-angled 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 = 1⁄2bh 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

prism is an object that has the same shape (or cross-section) for its whole length.

The volume of the prism equal to the area of the cross-section 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 r2 ) × h = π r 2h