    Question

# A regular hexagon of maximum possible area is cut off from an equilateral triangle. The ratio of area of triangle to the area of hexagon will be

A
32
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B
62
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C
32
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D
32
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Solution

## The correct option is D 32Each side is 4a. We can see that the area of the equilateral triangle is twice the area of a smaller right triangles. The right triangle's area is 1/2 base x height, and the height (b) is obtained through Pythagorus' Theorem from the other two sides. If we put that all together, we get:AT=2×(12×2a×b)=2a√(4a)2−(2a)2=2a√12a2=4a2√3Now let's look at the hexagon. You are right that it is made up of six equilateral triangles, so each side is 2a this time:Using the same logic as before, let's calculate the area of each small equilateral At=2×(12×a×c)=a√(2a)2−(a)2=a√3a2=a2√3We can see by this that the ratio of At is not half of AT it is 14 instead.Now when we look at the ratio of the area of the hexagon to the area of the large triangle, we get:6×AtAT=6a2√34a2√3At=32  Suggest Corrections  0      Similar questions  Related Videos   Basics Revisited
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