The corners of an equilateral triangular plate were cut in such a manner that it forms a regular hexagonal plate. What is the ratio of the area of the triangular plate to the area of the hexagonal plate?
A.5:3
B.4:3
C.3:2✓ Correct
D.2:1
Explanation
Cutting corners to form regular hexagon: cut equilateral triangles of side a/3 from each corner of original triangle of side a. Triangle area = (√3/4)a². Hexagon side = a/3, hexagon area = 6·(√3/4)(a/3)² = (√3/6)a². Ratio = (√3/4)/(√3/6) = 6/4 = 3:2.
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