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).
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A right-angled triangle
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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
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= 0.5 × base × height
= 1⁄2 × b × h
= 1⁄2bh
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The formulae for the area of three common quadrilaterals are given below:
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Shape
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Name |
Area |
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Parallelogram |
A = base × height = bh
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Rhombus |
A = base × height
= b × h
or
A = 1⁄2 × (product of length of diagonals)
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Trapezium |
A = 1⁄2 × ( a + b ) × h |
Volume of Prisms and Cylinders
A 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.
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Solid
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Name
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Volume
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Triangular
Prism
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V = (shaded area) × l
= ( 1⁄2 × b × h ) × l
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Cylinder
(circular prism)
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V = (shaded area) × h
= ( π r2 ) × h
= π r 2h
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