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

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Example
 
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Area of Triangles and Quadrilaterals

The area of triangles can be given by a formula:

Area

 

= 0.5 × base × height

= 12 × b × h

= 12bh

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

Shape
Name
Area

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Parallelogram

A = base × height bh

More_Measurement_area_04.gif

Rhombus

A = base × height

= b × h

or

A = 12 × (product of length of diagonals)

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Trapezium
 A = 12 × ( 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
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Triangular

Prism

V = (shaded area) × l

= ( 12 × b × ) × l

More_Measurement_volume_03.gif

Cylinder

(circular prism)

V = (shaded area) × h

= ( π r) × h

= π r 2h