question_answer

Two sides of a plot measuring 32 m and 24 m and the angle between them is a perfect right angle. the other two sides measure 25m each and the other  three angles are not right angles. The area of the plot in m2 is [SSC CGL Tier II, 2014]

A) 768

B) 534

C) 696.5

D) 684

Correct Answer: D

Solution :

[d] In \[\Delta ABC\]                                     \[AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}=\sqrt{{{(24)}^{2}}+{{(32)}^{2}}}\] \[=\sqrt{576+1024}=\sqrt{1600}=40\,cm\] Area of \[\Delta ABC=\frac{1}{2}\times 24\times 32=384{{m}^{2}}\] Area of \[\Delta ADC=\frac{b}{4}\sqrt{4{{a}^{2}}-{{b}^{2}}}\] \[=\frac{40}{4}\sqrt{4\times 625-1600}=10\sqrt{2500-1600}\]      \[=10\times \sqrt{900}\] \[22\,c{{m}^{2}}\] \[\therefore \]Required area of field \[=384+300=684\,{{m}^{2}}\]