Triangle:-
The area of a triangle, A is given by the formula

where b is the base and h is the height or the altitude.
If the lengths of the three sides of a triangle are known,  the area can be calculated using Hero's formula.

where a,b,c are the three sides of the triangle and s is the semi-perimeter,

If the three sides of the triangle are equal, the triangle is called an equilateral triangle and each angle is 60 degrees.
The area of an equilateral triangle is given by the formula

where a is the length of each side.
The altitude or height, h, of an equilateral triangle is

and the perimeter is

.

Square:-
A square consists of four equal sides and each side is perpendicular to the other, and opposite sides are parallel.
If a is the length of the side of a square, the are A is

Perimeter = 4a
Length of the diagonal is equal to

Rectangle.
A rectangle is a quadrilateral with opposite sides parallel to each other and each side perpendicular to the adjacent side. The opposite sides are equal.

Area = l x b (where l and b are the sides)
Perimeter = 2(l+b)
Length of the diagonal =

Parallelogram
Area of a trapezoid, A

There is also a formula for the area of a trapezoid, where the length of all sides are known:

http://en.wikipedia.org/wiki/Trapezoid wrote:

Another formula for the area can be used when all that is known are the lengths of the four sides. If the sides are a, b, c and d, and a and c are parallel (where a is the longer parallel side), then:

Last edited by Patrick (2006-04-04 01:42:02)

Quadrilateral

Area = 1/2 x (Product of diagonals) x (sine of the angle between them)

Area = 1/2 x diagonal x sum of the perpendiculars to it from opposite sides.

Parallelogram

Area = Base x Height

Area = Product of any two adjacent sides x (sine of the included angle)

Perimter = 2 (a+b) where a and b are the adjacent sides.

Rhombus

Area = 1/2 x Product of the diagonals

Area = Product of the adjacent sides x sine of the angle between them.

Trapezium

Area = 1/2 x (Sum of the parallel sides) x (height)

Regular Hexagon

where a=length of a side.

Circle Inscribed in a Triangle

The radius of a circle inscribed in a triangle of sides a, b, and c is given by

where the semiperimeter s of the triangle is given by

Circle Circumscribing a Triangle

The radius of a circle circumscribing a triangle of sides a, b, and c is given by

where once again s is the semiperimeter of the triangle.

Regular n-gon Inscribed in a Circle

The area of a regular n-gon inscribed in a circle of radius r is given by

The perimeter of the n-gon is given by

Regular n-gon Circumscribing a Circle

The area of a regular n-gon circumscribing a circle of radius r is given by

The perimeter of the n-gon is given by

Ellipse

The area of an ellipse of semi-major axis a and semi-minor axis b is given by

The perimeter of the ellipse is given by

or approximately

Rhombus:

Area, A is given by

where

are the two diagonals.


The perimeter, P, is given by the formula

ganesh wrote:

Length of the side, s is given by

This is wrong! It is

JaneFairfax,
Thanks for post #12. I have edited post #10.