Wednesday, 5 April 2017

How to Solve Questions on Change in Area of Quadrilaterals

SBI PO, IBPS and SSC Exam, all ask questions on quadrilaterals. Therefore it becomes only mandatory to pick up a trick or two about solving questions on quadrilaterals. 


Area of Quadrilaterals

Questions based on perimeter and area of quadrilaterals; find their way in most competitive exams. However, questions on quadrilaterals can be little bit if a challenge if you don’t remember the formulas to calculate the area and perimeter. But relax we have you covered!

So in our exclusive series of blog posts about smart methods that help you solve questions in 5- 10 seconds, the 8th Smart Method is about questions on Quadrilaterals.  We promise you that if you use this method to solve questions about area of quadrilateral, it won’t take you more than 10 seconds!
Area of Quadrilaterals

Area of Quadrilaterals

A quadrilateral is a closed four sided figure having two dimensions. Some common quadrilaterals are- Square, Rectangle, Parallelogram, Rhombus and Trapezium. As students most of us study the different kinds of quadrilaterals during high school and cram their properties and formulas to be able to solve questions on Quadrilaterals.


Formulas for Area of Quadrilaterals

Area of Quadrilaterals
Area of Quadrilaterals
Area of Quadrilaterals
Area of Quadrilaterals
Area of Quadrilaterals

Example of a Question on Area of Quadrilaterals

The length of a rectangle is increased by 40% and its breadth increased by 20%.  What will be the percentage increase in the area of the rectangle?
1) 50%     2)10%     3) 44%     4) 68%     5) None of these

 Conventional Method to Solve Questions on Quadrilaterals

On reading the above question most of us would quickly assume values for the length and breadth of the rectangle, then increase then by the given values, apply the formula for the area of the quadrilateral, calculate the new area and then find the change based on the given values. Let’s see the steps involved-
Assuming the Length and Breadth of the rectangle to be L an B respectively,

Step 1:
Area of the rectangle= L x B= LB

Step 2:
New length of the rectangle= L+ 40%= 1.4L

Step 3:
New breadth of the rectangle= B+ 20%= 1.2B

Step 4:
New area of the rectangle= 1.4L x 1.2B= 1.68

Step 5:
Percentage of increase in the area= {(New Area- Old Area)/ Old Area}X 100

Step 6:
{(1.68LB- LB)/LB} x100= .68x 100= 68%
Phew! Trust me that was a lot of calculation of a problem as simple as that.

Smart Method to Solve Questions on Area of Quadrilaterals

Let’s discuss how we can reduce these 40 seconds to 15 seconds or even less by using the concept of effective percentage, the formula for which is = A+ B+ (AxB)/100.
Assuming change in length and breadth to be A and B respectively, A= 40, B= 20

Step 1:
Percentage change in area= 40+ 20 + (40x 20)/100= 60+ (800/100)= 68%

Wasn’t that quick and simple! 
Area of Quadrilaterals

Time to try some questions using the time saving smart method you just learnt!

Question 1:  The length of a rectangle is increased by 20% and its breadth increased by 10%.
What will be the percentage increase in the area of the rectangle?
1)23%      2)25%      3) 32%      4) 30%      5) None of these

Question 2:  The length of a rectangle is increased by 50% and its breadth decreased by 20%. What will be the percentage increase in the area of the rectangle?
1) 10%      2)20%      3) 30%      4) 40%      5) None of these

Do write your answers in the comment section and tell us how you liked this smart method to solve questions on quadrilaterals.

Keep watching this space for more smart methods and keep practicing using smart methods.
Area of Quadrilaterals




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