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Q143 (IAS/1995) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

In the Cartesian plane four points P, Q, R, S have co-ordinates (1, 1), (4, 2), (4, 4) and (1, 4). The area of the quadrilateral PQRS is

Result
Your answer: —  Â·  Correct: B
Explanation

The four given points lie in the Cartesian coordinate system, so their polygonal area can be computed directly from coordinates [1]. Use the shoelace (Gauss) formula for a quadrilateral with vertices listed in order: area = 1/2 |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|. For P(1,1), Q(4,2), R(4,4), S(1,4): sum1 = 1*2 + 4*4 + 4*4 + 1*1 = 35; sum2 = 1*4 + 2*4 + 4*1 + 4*1 = 20. Thus area = 1/2 |35 - 20| = 7.5 square units. Hence option 2 is correct; diagonal lengths are not required when coordinates are known.

Sources

  1. [1] Exploring Society:India and Beyond. Social Science-Class VI . NCERT(Revised ed 2025) > Chapter 1: Locating Places on the Earth > LET'S EXPLORE > p. 14
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