PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Straight Lines · medium

The area of the quadrilateral with vertices (0,0), (4,0), (5,3) and (0,3) is

Single correct option

The area of the quadrilateral with vertices (0,0)(0,0), (4,0)(4,0), (5,3)(5,3) and (0,3)(0,3) is
  1. A. 272\dfrac{27}{2}
  2. B. 1212
  3. C. 1515
  4. D. 99
Show answer and solution

Answer: (A) 272\dfrac{27}{2}

Apply the shoelace formula in order: 12∣(0⋅0+4⋅3+5⋅3+0⋅0)−(0⋅4+0⋅5+3⋅0+3⋅0)∣=272\dfrac12\left|(0\cdot0+4\cdot3+5\cdot3+0\cdot0)-(0\cdot4+0\cdot5+3\cdot0+3\cdot0)\right|=\dfrac{27}{2}. Alternatively it is a trapezium with parallel sides 44 and 55 and height 33, so the area is 12(4+5)⋅3=272\dfrac12(4+5)\cdot3=\dfrac{27}2. The value 1212 is the rectangle 4×34\times3, and 1515 is the rectangle 5×35\times3; neither equals the trapezium because the slanted side cuts off a triangle.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake