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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 = 2r 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 = r BACK |