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

Sum of the Sides

4. Cylinder :

5. Cone :

6. Sphere :

7. Hemi Sphere :

- 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.

Students can learn and improve on their skillset for using Verbal Ability effectively and can also prepare for competitive examinations like...

- All I.B.P.S and Public Sector Bank Competitive Exam
- Common Aptitude Test (CAT) Exams
- UPSC Paper-II or CSAT Exams
- SSC Competitive Exams
- Defence Competitive Exams
- L.I.C / G.I.C AAO and Clerk Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- Career Aptitude Test (IT Companies) and etc.