S1


Angles:
The total of all exterior angles on any polygon is 360°.
Therefore, it can be said that in a regular polygon, each exterior angle = 360/n where n is the number of sides.
There are 180° on a straight line.
Therefore the general formula to work out each angle in a regular polygon is 180° - 360/n.

Example:
Nonagon = 180° - 360 ÷ 9 = 140°

The formula to work out the total of the interior angles is 180(n-2) where n is the number of sides.

Right Angled Triangles:

According to the Greek mathematician, Pythagoras, there is a general formula to work out the length of the longest side of a right angled triangle, opposite the right angle.
If a and b are the other sides and c is the hypotenuse, the following is true:
a² + b² = c²
Therefore c = sqrt (a² + b²)

Example:
5² + 12² = 13²


2 Dimensional Shapes - Area and Perimeter Formulae:
Circle:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cpi%20r%5E%7B2%7D
Perimeter:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%202%5Cpi%20r%5E%7B2%7D
Triangle:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cfrac%7Bbh%7D%7B2%7D
Rectangle:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20lw
Perimeter:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%202(l+w)
Trapezium:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cfrac%7B%5Csum(parallel)(perp.height)%7D%7B2%7D
Parallelogram:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20bh
Perimeter:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%202(l+w)
Kite:
Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cfrac%7Bbh%7D%7B2%7D
3 Dimensional Shapes - Volume and Surface Area:
Sphere:
Volume: external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B2%7D


Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%204%5Cpi%20r%5E%7B2%7D

Cylinder:
Volume:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cpi%20r%5E%7B2%7Dh
Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%202%5Cpi%20r(r+h)
Cone:
Volume:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%200.5%5Cpi%20rh
Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20%5Cpi%20r(r+h)
Square Based Pyramid:
Volume:
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Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20b(b+2(slant))
Cube:
Volume:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20x%5E%7B3%7D
Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%206x%5E%7B2%7D
Cuboid:
Volume:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%20lwh
Surface Area:
external image gif.latex?%5Cfn_cm%20%5Cbg_white%20%5C300dpi%20%5Cinline%202(l(h+w)+hw)
BY MUHAMMED