Quantitative Aptitude Ques 23

Question: A piece of wire 132 cm long is bent successively in the shape of an equilateral triangle, a square, a circle and a regular hexagon. The largest area is included when the wire is bent into the shape of a [FCI (Assistant) Grade III 2015]

Options:

A) circle

B) hexagon

C) square

D) triangle

Show Answer

Answer:

Correct Answer: A

Solution:

  • Area of equilateral triangle $ =\frac{\sqrt{3}}{4}\times {{( \frac{132}{3} )}^{2}} $ $ =\frac{\sqrt{3}}{4}\times {{(44)}^{2}}=484\sqrt{3},cm^{2} $ Area of square $ ={{( \frac{132}{4} )}^{2}}=1089,cm^{2} $ Area of circle $ =\frac{22}{7}\times 441=1386,cm^{2} $ Area of regular hexagon $ =\frac{\sqrt{3}}{4}\times 6\times {{( \frac{132}{6} )}^{2}} $ $ =\frac{\sqrt{3}}{4}\times 6\times {{(22)}^{2}}=\frac{\sqrt{3}}{4}\times 6\times 484 $ $ =\frac{2904\sqrt{3}}{4}=726\sqrt{3},cm^{2} $ Hence, circle contains the largest area.
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