Areas
Posted by
Ravi Kumar at Monday, November 24, 2008
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Important Facts and Formulae:
Results On Triangle
1.Sum of the angles of a triangle is 180 degrees.
2.The sum of any two sides of a triangle is greater
than third side.
3.Pythagoras Theorem:
In a right angled triangle (Hypotenuse)2 = (Base)2 +(Height)2
4.The line joining the mid point of a side of a triangle
to the opposite vertex is called the MEDIAN.
5.The point where the three medians of a triangle meet,
is called CENTROID. The centroid divides each of the
medians in the ratio 2:1
6.In an isosceles triangle, the altitude from the
vertex bisects the base
7.The median of a triangle divides it into two triangles
of the same area.
8.The area of the triangle formed by joining the mid points
of the sides of a given triangle is onefourth of the area
of the given triangle.
Results On Quadrilaterals
1.The diagonals of a Parallelogram bisect each other.
2.Each diagonal of a Parallelogram divides it into two
triangles of the same area.
3.The diagonals of a Rectangle are equal and bisect
each other
4.The diagonals of a Square are equal and bisect each
other at right angles.
5.The diagonals of a Rhombus are unequal and bisect
each other at right angles.
6.A Parallelogram and a Rectangle on the same base
and between the same parallels are equal in area.
7.Of all he parallelogram of given sides the parallelogram
which is a rectangle has the greatest area.
Formulae:
1.Area of a RECTANGLE = length * breadth
Length = (Area/Breadth) and Breadth = (Area/Length)
2.Perimeter of a RECTANGLE = 2(Length + Breadth)
3.Area of a SQUARE = (side)2 = Â½ ( Diagonal)2
4.Area of four walls of a room = 2(length + breadth) * height
5.Area of a TRIANGLE = Â½ * base * height
6.Area of a TRIANGLE = âˆš[s * (sa) * (sb) * (sc)],
where a,b,c are the sides of the triangle and s = 1/2(a+b+c)
7.Area of EQUILATERAL TRIANGLE = âˆš(3/4)* (side)2
8.Radius of in circle of an EQUILATERAL TRIANGLE of
side a = r / 2âˆš3
9.Radius of circumcircle of an EQUILATERAL TRIANGLE
of side a = r / âˆš3
10.Radius of incircle of a triangle of area âˆ† and
semi perimeter S = âˆ† / s
11.Area of a PARALLELOGRAM = (base * height)
12.Area of RHOMBUS = 1/2 (product of diagonals)
13.Area of TRAPEZIUM =
=1/2 * (sum of parallel sides)* (distance between them)
14.Area of a CIRCLE = ï›‡ r2 where r is the radius
15.Circumference of a CIRCLE = 2ï›‡r
16.Length of an arc = 2 ï›‡rÃ¸ / 360, where Ã¸ is central angle
17.Area of a SECTOR = Â½ (arc * r) = ï›‡r2Ã¸ / 360
18.Area of a SEMICIRCLE = ï›‡r2 / 2
19.Circumference of a SEMICIRCLE = ï›‡r