Shortcut Tricks To Solve Mensuration

Shortcut Rules to Solve Problems on Mensuration

Effective for IBPS PO - SBI PO Exam

Dear Reader,

Here we will start a series of Quantitative Aptitude Shortcut Tricks for your upcoming SBI - IBPS - SSC and Other Government Competitive Exams. We will try to cover up all topics of the quantitative Aptitude Sections from which question was generally asked.

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Trick - 1

• If a, b and c are lengths of the sides of a triangle and S=$\frac{1}{2}\left( a+b+c \right)$, then Area of the triangle 

$\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right).}$

Trick - 2

• To find the area and perimeter of a rectangle if its one side and one diagonal are given

(1) Area of rectangle $=\left( l\times \sqrt{{{d}^{2}}-{{I}^{2}}} \right)sq$ units.
(2) Perimeter of rectangle $=2\left( l+\sqrt{{{d}^{2}}-{{I}^{2}}} \right)units.$ 

Trick - 3

• There is a rectangle of area 'A' sq unit. If the sum of its diagonal and length is n times of its breadth, then the length and breadth of the rectangle are $\sqrt{\frac{A({{n}^{2}}-1)}{2n}}$ and $\sqrt{\frac{2An}{{{n}^{2}}-1}units}$  respectively. 

Trick - 4

• Length of a rectangle is increased by 'a' units and breadth is decreased by 'b' units, area of the rectangle remains unchanged. If length be decreased by 'c' units and breadth be increased by 'd' units, in this case also area of the rectangle remains unchanged. Length and breadth of the rectangle are given by $ac\left( \frac{d+b}{ad-bc} \right)$ and $bd\left( \frac{a+c}{ad-bc} \right)units$  respectively.

Trick - 5 

• There is a rectangle. Its length is 'x' units more than its breadth. If its length is increased by 'y' units and its breadth is decresed by 'z' units, the area of the rectangle is unchanged. Length and breadth of the rectangle are $\left[ \frac{\left( x+z \right)y}{y-z} \right]$ and $\left[ \frac{\left( x+y \right)z}{y-z} \right]units$ respectively. 

   

Trick -6

• To find perimeter of a rhombus if the length of the two diagonals are given. 

Perimeter of the rhombus

$=2\sqrt{\left( {{d}_{1}}^{2}+{{d}_{2}}^{2} \right)}$ units.

Where, ${{d}_{1}}$ and ${{d}_{2}}$ are the two diagonals.
 

Questions for Practice

Q1. Find the area of a triangle whose sides are 50 metres, 78 metres, 112 metres respectively and also find the perpendicular from the opposite angle on the side 112 metres. 

Q2. One side and the diagonal of a rectangle are 40 m and 50 m respectively. Find its area and perimeter.

Q3. There is a rectangular field of area 60 sq cm. Sum of its diagonal and length is 5 times of its breadth. Find the breadth of the rectangular field.

Q4.Length of a rectangular field  is increased by 7 m and breadth is decreased by 3 m area of the rectangle remains unchanged. If length be decreased by 7 m and breadth be increased by 5 m, again area remains unchanged. Find the length and breadth of the rectangular field. 

Q5. Length of a rectangular black-board is 8 cm more than that of its breadth. If its length is increased by 7 cm and its breadth is decreased by 4 cm, its area remains unchanged. Find the length and breadth of the rectangular blackboard.

Q6. In a rhombus, the length of the two diagonals are 40 m and 30 m respectively. Find its perimeter.

Answers

Answer 1. 30 metres

Answer 2. 140 metres

Answer 3. 5 cm

Answer 4. 15 metres
Answer 5. 28 cm, second method  20 cm 

Answer 6. 100 m