﻿ Area - Facts and Formulae
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# Area - Facts & Formulae

## I.FACTS ON TRIANGLES:

1. Sum of the angles of a triangle is 180 degrees.
2. Sum of any two sides of a triangle is greater than the third side.
3. Pythagoras theorem:
In a right angle triangle,
(Hypotenuse)^2 = (base)^2 + (Height)^2
4. The line joining the midpoint 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.
Centroid divides each of the medians in the ratio 2:1.
6. In an isosceles triangle, the altitude from the vertex bi-sects the base
7. The median of a triangle divides it into two triangles of the same area.
8. Area of a triangle formed by joining the midpoints of the sides of a given triangle is one-fourth of the area of the given triangle.

## II.FACTS ON QUADRILATERALS:

1. The diagonals of a parallelogram bisects 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 the parallelograms of a given sides , the parallelogram which is a rectangle has the greatest area.

## FORMULAES

• .Area of a rectangle=(length*breadth)
• Perimeter of a rectangle = 2*(length+breadth)
• Area of a square = (side)2 =½(diagonal)2
• Area of four walls of a room = 2*(length + breadth)*(height)
• Area of the triangle=1/2(base*height)
• Area of a triangle = √(s*(s-a)(s-b)(s-c))
where a,b,c are the sides of a triangle and s= ½(a+b+c)
• Area of the equilateral triangle =√(3/4) * (side)2
• Radius of circle of an equilateral triangle of side a = a/2 √3
• Radius of circumcircle of an equilateral triangle of side a = a / √3
• Radius of circle of a triangle of area del and semi perimeter S=del/S
• Area of the parlelogram =(base *height)
• Area of the rhombus = ½(product of the diagonals)
• Area of the trapezium = ½(size of parallel sides)*distance between them
• Area of a circle =∏*r2,where r is the radius
• Circumference of a circle = 2*∏*R.
• Length of an arc = 2∏*R* é/(360) where é is the central angle
• Area of a sector = (½) (arc x R) = ∏*R^2*é/360. where é is the central angle
• Area of a semi-circle = (∏)*R2
• Circumference of a semi-circle = (∏)*R.