Area Formulas

FUNDAMENTAL CONCEPTS

1. Results on Triangles:

  1. Sum of the angles of a triangle is 180°.
  2. The sum of any two sides of a triangle is greater than the 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 positive vertex is called the median.
  5. The point where the three medians of a triangle meet, is called centroid. The centroid divided 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.

 2. Results on Quadrilaterals:

  1. The diagonals of a parallelogram bisect each other.
  2. Each diagonal of a parallelogram divides it into 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 parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

IMPORTANT FORMULAE

I.  1. Area of a rectangle = (Length x Breadth).

    Length =98 and Breadth = 99

2. Perimeter of a rectangle = 2(Length + Breadth).

II. Area of a square = (side)2 = (diagonal)2.

III. Area of 4 walls of a room = 2 (Length + Breadth) x Height.

IV.    1.  Area of a triangle = x Base x Height.

  2. Area of a triangle = 100

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

  3.  Area of an equilateral triangle = 101 x(side)²

  4.  Radius of in circle of an equilateral triangle of side a = 102

  5.   Radius of circumcircle of an equilateral triangle of side a = 103

  6. Radius of incircle of a triangle of area and semi-perimeter s = 104

V.   1.  Area of parallelogram = (Base x Height).

  2.  Area of a rhombus = x (Product of diagonals).

 3.   Area of a trapezium = x (sum of parallel sides) x distance between them.

VI.    1.  Area of a circle = R² ,  where R is the radius.

   2.   Circumference of a circle = 2R.

   3.   Length of an arc = 105 where is the central angle.

   4. Area of a sector = 1-div-1by2 (arc x R)= 106

VII. 1.   Circumference of a semi-circle = R.

              2.   Area of semi-circle = 107

 

 


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