XAT 2016 — QA & DI Question 5
HexagonEasy
âABC and âXYZ are equilateral triangles of 54 cm sides. All smaller triangles like âANM, âOCP, âQPX etc. are also equilateral triangles. Find the area of the shape MNOPQRM.
âââââââ
Answer & solution
243√3 sq. cm.
- B
486√3 sq. cm.
- C
729√3 sq. cm.
- D
4374√3 sq. cm.
- E
None of the above
Solution
Since all triangles are equilateral triangles
This is possible when YM = MN = NZ = 1/3 of YZ = 54/3 = 18 cm.
∴ Side of the regular hexagon MNOPQRM is 18 cm.
∴ Area of the hexagon = 6 × √3/4 × (18)2 = 486√3.
Hence, option (b).