Allied & ICAR Exam Bank • ALLIED_2449 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Data Interpretation

Question Statement:

In a radar polygon with vertices at $(r_1, \theta_1), (r_2, \theta_2), \dots$, an engineer computes the polygon area for a 3-axis radar chart with values $r_1 = 6, r_2 = 8, r_3 = 10$ and equal angles of $120^\circ$. The total area of the triangular radar plot is:

Options:

  • (A) $47\sqrt{3} \approx 81.4$
  • (B) $40\sqrt{3}$
  • (C) $52\sqrt{3}$
  • (D) $45\sqrt{3}$

Answer Key:

A

Step-by-Step Solution & Explanation

Area $= \frac{1}{2} \sin(120^\circ) [r_1 r_2 + r_2 r_3 + r_3 r_1] = \frac{1}{2} (\frac{\sqrt{3}}{2}) [48 + 80 + 60] = \frac{\sqrt{3}}{4} [188] = 47\sqrt{3} \approx 81.4$.
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