An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1, i.e. 66.66%
Let the side of the triangle be a
Side of the hexagon = b
therefore, a = 3b
b = a/3
Now,
√3/4 a2 = 300
⇒ a2 = 400√3
⇒ b2 = a2/9 = 400√3/9
Area of hexagon = 6 × √3/4 b2 = 6 × √3/4 × 400√3/9 = 200
Hence,
Required percentage = 200/300 × 100 = 66.67%