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 :
Area of a square inscribed in a circle of radius r is 2r2.
Side of a square inscribed in a circle of radius r is √2 r.
The ares of the largest triangle inscribed in a semi-circle of radius r is r2.
The area of the largest circle that can be drawn in a square of side X is π(x/2)2.
The area of a circle circumscribed in an equuilateral triangle of side X is π/3 X2;
The area of a circle inscribed in an equuilateral triangle of side X is π/12 x2.
If the area of a square is X Sq.Cm. then area of the circle formed by the same perimeter is 4X/π Cm3.
Relation between Circumference (C) and Area (A) of a circle is C2 = 4πA
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.
The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is 6 : π.
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.
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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Important Mensuration Formulas Question and Answers
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