Geometry and Mensuration Formulas & Properties – APSC PrelimCSAT Paper Notes, formulas

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Geometry and Mensuration Important Formulas

& Properties – 

Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams

Go to Aptitude, Reasoning and Quants Formulas & Notes

 

Circle
  • Area of a circle = R2, where R is the radius.
  • Circumference of a circle = 2πR.
  • Length of an arc =  2 π r ×  (θ/360°), where θ is the central angle.
  • Area of a sector = θ/2 × r2.
  • Perimeter of a semi-circle =πR + 2R.

 

Quadrilaterals

Parallelogram

  • Area of parallelogram = (Base x Height).
  • The diagonals of a parallelogram bisect each other.
  • Each diagonal of a parallelogram divides it into triangles of the same area.
  • A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
  • Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

Rectangle

  • Area of a rectangle = (Length x Breadth).
  • Perimeter of a rectangle = 2(Length + Breadth).
  • The diagonals of a rectangle are equal and bisect each other.

Square

 

  • Area of a square = (side)2 = (diagonal)2.
  • Area of 4 walls of a room = 2 (Length + Breadth) x Height.
  • The diagonals of a square are equal and bisect each other at right angles.

Rhombus

  • Area of a rhombus = x (Product of diagonals).
  • The diagonals of a rhombus are unequal and bisect each other at right angles.

Trapezium

  • Area of a trapezium =  (sum of parallel sides)/2 x distance between them.

 

Triangle

 

  • Sum of the angles of a triangle is 180°.
  • The sum of any two sides of a triangle is greater than the third side.
  • Area of a triangle = x Base x Height.
  • 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).
  • Area of an equilateral triangle = sqrt(3)/4 x (side)2.

Pythagoras Theorem

In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.

  • Median – The line joining the mid-point of a side of a triangle to the opposite vertex is called the median.
  • Centroid – The point where the three medians of a triangle meet. The centroid divided each of the medians in the ratio 2 : 1.
  • In an isosceles triangle, the altitude from the vertex bisects the base.
  • The median of a triangle divides it into two triangles of the same area.
  • 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.