My Tax & Diary

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)
    Therefore length = (area/breadth) and breadth=(area/length)
  • 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.









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