Important Mensuration Formulas

1. Rectangle : Two opposite sides are equal, diagonals are equal. Each angle is 90°


2. Rhombous: 


3. Square : All sides, diagonals, angles are equal.

4. Parallelgram : Two opposite sides are parallel AD//BC and AB//DC


5. Triangles :


6. Trapezium : One porallel side equal AB//CD

Area = 1/2 h (a + b) = 1/2 (Sum of Parallel sides × distance between them)
Sum of the Sides

7. Equilateral triangle : :



1. Prism : 

2. Cube : 

3. Cuboid : 


4. Cylinder : 


5. Cone : 

6. Sphere : 

7. Hemi Sphere : 



1. Circle :



2. Semicircle :



3. Sector :

 
  1. Area of a square inscribed in a circle of radius r is 2r2.
  2. Side of a square inscribed in a circle of radius r is √2 r.
  3. The ares of the largest triangle inscribed in a semi-circle of radius r is r2.
  4. The area of the largest circle that can be drawn in a square of side X is π(x/2)2.
  5. The area of a circle circumscribed in an equuilateral triangle of side X is π/3 X2;
  6. The area of a circle inscribed in an equuilateral triangle of side X is π/12 x2.
  7. If the area of a square is X Sq.Cm. then area of the circle formed by the same perimeter is 4X/π Cm3.
  8. Relation between Circumference (C) and Area (A) of a circle is C2 = 4πA
  9. An equilateral triangle is circumscribed by a circle and another circle is inscribed in that triangle.
    Then the ratio of the areas of the two circles is 4 : 1.
  10. The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is 6 : π.
  11. A cube of maximum volume is cut from a sphere then the ratio of the volumes of the cube and the sphere is 2 : √3 π.
  12. Two circular cylinders of equal volume have their heights in ratio of a : b then the ratio of their is √b : √a.

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