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.