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Q.

A regular hexagon of maximum possible area is cut off from equilateral triangles; the ratio of area of triangle to the area of hexagon will be


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a

2:2

b

2:3

c

5:2

d

None  

answer is A.

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Detailed Solution

Let 3a = side of equilateral the area of the triNGLE =
√ 3/4 =a2
√3/4 ×(3a)2
= 9√3/4 a2
Question ImageWe know that a regular hexagon is formed by joining 6 equilateral triangles .
Hence side of regular hexagon inscribed form an equilateralPQR = 3a/3 = 9 cm
Area of PQR = Area of hexagon ABCDEF = 6×√3/4 ×a2
= 6√3/4 a2
Area of PQR / Area of hexagon ABCDEF
= 9√3/A2/ 4×6√3×A2/4 = 3/2
 
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