Concept of Trigonometry

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.

                                                  

Formula

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 = (a+b-c)/2

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 = 2 π r where r is the radius

15. Circumference of a CIRCLE = 2 π r

16. Length of an arc = 2 πr/ 360 

17. Area of a SECTOR = ½ (arc * r) = π r2 / 360

18. Area of a SEMICIRCLE = 1/2 π r²

19. Circumference of a SEMICIRCLE = π r

                                                  

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