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Tuesday, June 30, 2015

UPSC Maths Problems Challenge : A Problem A Day! (Day 18)

Today's problem is also from the Prelims section of IAS exam conducted by UPSC and is from co-ordinate geometry,which I believe is one of the most interesting sections of Maths I have been introduced to so far.I hope you all find this useful.Read on to find out the solution.





Today's Problem(30/06/2015)


Question Credit : http://mrunal.org/


[1995] In the Cartesian plane, four points P,Q,R,S have co-ordinates (1,1), (4,2), (4,4) and (1,4) respectively. The area of the quadrilateral PQRS is ?
The area of triangle PQR = |1/2[ (1) (2 - 4) + 4 (4 - 1) + 4 (1 - 2)] | sq.units = 1 sq.unit
The area of triangle PRS  = |1/2[ (1) (2 - 4) + 4 (2 - 4) + 1 (1 - 2)] | sq.units = 6.5 sq.units
Area of quadrilateral PQRS = The area of triangle PQR + The area of triangle PRS
= (1 + 6.5) sq.units = 7.5 sq.units
So,the area of quadrilateral PQRS is 7.5 sq.units.


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