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::Important Formulas

Here Some Basic Formulas/Rules Are given below :-

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

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

    1. Area of a square = (side)2 = 1/2(diagonal)2.

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

    1. Area of a triangle = 1/2 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 = 1/2 (a + b + c).

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

    4. Radius of incircle of an equilateral triangle of side a = a/2√3

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

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

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

    2. Area of a rhombus = 1/2 X (Product of diagonals).

    3. Area of a trapezium = 1/2 X (sum of parallel sides) X distance between them.

    1. Area of a circle = πR2, where R is the radius

    2. Circumference of a circle = 2πR.

    3. Length of an arc = = 2πRo/360 where o is the central angle.

    4. Area of a sector = = 1/2 (arc X R) = πR2o /360

    1. Area of a semi-circle = πR2/2

    2. Circumference of a semi-circle = πR.


    1. Results on Triangles :

    2. Sum of the angles of a triangle is 180°.
    3. The sum of any two sides of a triangle is greater than the third side.
    4. Pythagoras Theorem : In a right-angled triangle,
      (Hypotenuse)2 = (Base)2 + (Height)2
    5. The line joining the midi-point of a side of a triangle to the oppasite vertex is called the median.
    6. 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.
    7. In an isosceles triangle, the altitude from the vertex bisects the base.
    8. The median of a triangle divides it into two triangles of the same area.
    9. 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.
    1. Results on Quadrilaterals :

    2. The diagonals of a parallelogram bisect each other.
    3. Each diagonal of a parallelogram divides it into two triangles of the same area.
    4. The diagonals of a rectangle are equal and bisect each other.
    5. The diagonals of a square are equal and bisect each other at right angles.
    6. The diagonals of a rhombus are unequal and bisect each other at right angles.
    7. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
    8. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

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