AREAS

AREAS

Important Facts and Formula: 

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 one-fourth 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 = ½ ( Diagonal)2

4.Area of four walls of a room = 2(length + breadth) * height

5.Area of a TRIANGLE = ½ * base * height

6.Area of a TRIANGLE = √[s * (s-a) * (s-b) * (s-c)],

where a,b,c are the sides of the triangle and s = 1/2(a+b+c)

7.Area of EQUILATERAL TRIANGLE = √(3/4)* (side)2

8.Radius of in circle of an EQUILATERAL TRIANGLE of 

side a = r / 2√3

9.Radius of circumcircle of an EQUILATERAL TRIANGLE 

of side a = r / √3

10.Radius of incircle of a triangle of area ∆ and 

semi perimeter S = ∆ / 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 =  r2 where r is the radius

15.Circumference of a CIRCLE = 2r

16.Length of an arc = 2 rø / 360, where ø is central angle

17.Area of a SECTOR = ½ (arc * r) = r2ø / 360

18.Area of a SEMICIRCLE = r2 / 2

19.Circumference of a SEMICIRCLE = 