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Question

Three equilateral triangles are cut from an equilateral triangle of area 36 cm2 such that a regular hexagon is left. Find the area of hexagon (in cm2 )

A
24
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B
28
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C
30
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D
32
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Solution

The correct option is B 24
Given that:
Area of ABC=36cm2
To find:
Area of the hexagon=?
Solution:
Let a be length of the side equilateral ABC
Then, length of the side of the smaller equilateral triangle =a3
ar(ABC)=36cm2
or, 34a2=36cm2
or, a2=36×43cm2
Now,
Area of the hexagon= Area of ABC3× Area of smaller triangle
=36cm23×34×(a3)2
=36cm234×36×43×3cm2
=36cm212cm2
=24cm2
So, Area of the hexagon =24cm2
Hence, A is the correct option.

643169_395403_ans_4492a68e82844821b47c2b9a69c6ae94.png

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