Aptitude - Area

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

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

          Length = Area and Breadth = Area .
    Breadth Length

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

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

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

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

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

    3.   Area of an equilateral triangle = 3 x (side)2.
    4

    4.   Radius of incircle of an equilateral triangle of side a = a .
    23

    5.   Radius of circumcircle of an equilateral triangle of side a = a .
    3

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

  5. 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.

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

    2.   Circumference of a circle = 2R.

    3.   Length of an arc = 2R , where is the central angle.
    360

    4.   Area of a sector = 1 (arc x R) = R2 .
    2 360

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

    2.   Area of semi-circle = R2 .
    2