Home / Arithmetic Aptitude / Area :: Important Formulas

Arithmetic Aptitude :: Area

Area - Important Formulas

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FUNDAMENTAL CONCEPTS

1. Results on Triangle

  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 opposite 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.

  9. 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

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

  2.     Length = \([\frac { Area } { Breadth } ]\)and Breadth =\([\frac { Area } { Length } ]\)

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

  4. Area of a square = (side)2 =  \( \frac { 1 } { 2 } \)(diagonal)2.

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

  6. 1.   Area of a triangle =  x \( \frac { 1 } { 2 } \)Base x Height.

    2.   Area of a triangle = s(s-a)(s-b)(s-c)
          where abc are the sides of the triangle and s = \( \frac { 1 } { 2 } \)(a + b + c).

  7.   3 . Area of an equilateral triangle = \( \frac { \sqrt3} { 4 }\) x (side)2.

     4. Radius of incircle of an equilateral triangle of side a =\( \frac { a} { 2 \sqrt3 }\)

    5.  Radius of circumcircle of an equilateral triangle of side a =\( \frac { a} { \sqrt3 }\)

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

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

             2.  Area of a rhombus =\( \frac { 1 } { 2 } \) x (Product of diagonals)

             3 .Area of a trapezium = \( \frac { 1 } { 2 } \)x (sum of parallel sides) x distance between them

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

           2.   Circumference of a circle = 2

  8.        3. Length of an arc = \( \frac {2 \pi R} { 360 } \)where  is the central angle.360

  9.      Circumference of a semi-circle = R.