# Quantitative Aptitude: Tips & Strategy- Some Properties of Parallelograms, Triangles & Circles

The experts of Jagranjosh.com have evolved forward to help the aspirants in attempting all the questions speedily with basic preparatory strategy. By providing basic concepts, we are trying to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some properties can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam. Here are some important properties of Parallelograms, Triangles and Circles

- The diagonals of parallelogram bisect each other.
- Each diagonal of the parallelogram divides it into two triangles of equal area.
- The diagonals of a rectangle are of equal lengths and they bisect each other.
- The diagonals of a square are equal and they bisect each other at right angles.
- A rhombus has unequal diagonals and they bisect each other at right angles.
- A parallelogram and a rectangle have equal areas, if they are on the same base and between the same parallel lines.
- Opposite angles are equal in a parallelogram but they are not right angles.
- * If the length and breadth of a rectangle are increased by a% and b% respectively, then area will be increased by
- [For decrease take negative sign]
- * If all the increasing sides of any two-dimensional figure are changed by a%, then its area will be changed by
. In case of circle, radius (or diameter) is increased in place of sides. [For decrease take negative sign] - * If all the measuring sides of any two-dimensional figure are changed (increased or decreased) by a%, then its perimeter also changes by a%. In case of circle such change takes palce because of the change in radius (or diameter).
- * If area of a square is a sq unit, then the area of the circle formed by the same perimeter is given by
sq unit. - * Area of a square inscribed in a circle of radius r is equal to 2r
^{2}. - * The area of the largest triangle inscribed in a semi-circle of radius r is equal to r
^{2}. - * If the side of equilateral triangle is a cm, then radius of circle circumscribing the triangle,
cm and radius of circle inscribed in the triangle, . - * The area of the largest circle that can be drawn in a square of side a is
- * If a pathway of width
*x*is made inside or outside a rectangular plot of length*l*and breadth*b*, then area of pathway is - (i) 2
*x*(*l*+*b*+ 2*x*), if path is made outside the plot. - (ii) 2
*x*(*l*+*b*– 2*x*), if path is made inside the plot. - * If two paths, each of width x are made parallel to length (
*l*) and breadth (*b*) of the rectangular plot in the middle of the plot, then area of the paths is*x*(*l*+*b*–*x*).