Indian Institute of Foreign Trade 2016 Solved Paper

Question : 10 of 123

Marks: +1, -0

Let PQRSTU be a regular hexagon. The ratio of the area of the triangle PRT to that of the hexagon PQRSTU is

Solution:

(b) Let the side of hexagon PQRSTU is ‘a’
∴ Area of hexagon

= 6 × { √{ 3 } }/ { 4 } × a ^ { 2 }

The side of triangle PRT =

√3a

∴ Area of △PRT

= { √ { 3 } } /{ 4 } × ( √ { 3 } a ) ^ { 2 } = { 3 √ { 3 } } /{ 4 } a ^ { 2 }

∴ Reqd. ratio is

{ 3 √ { 3 } }/ { 4 } a ^ { 2 } × { 4 }/ { 6 √{ 3 } a ^ { 2 } } = { 3 }/ { 6 } = { 1 } /{ 2 } = 0.5

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