CAT 2003 Slot 1 — QA Question 33
HexagonEasy
In the figure below, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?
Answer & solution
Correct answer: 1 12
- B
- C
- D
Solution
We can see that triangles AMF, AMB, BMC, CMD, DME and EMF are all equilateral triangles. Also, AE, XY and BD bisect MF, AB, ED and CM.
∴ All the small right triangles in the figure are congruent.
∴ A(âAOF) = × the area of the hexagon ABCDEF
Hence, option (a).