Hexagon Again

Geometry Level 1

ABCDEF is a regular hexagon. O is a point in the hexagon such that FO is parallel to ED and AOF is a right angle. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

1/18 1/24 1/12 1/6

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Sanjeet Raria by Sanjeet Raria , 27, India

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2 solutions

Heather Martin
Aug 24, 2014

There are six equilateral triangles in a hexagon and this triangle is half of one equilateral triangle so 2x6=12 and so there are 12 AOF triangles

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The triangle is 1/2 one of the 6 triangles that form the hexagonal.

Khairy Wanas - 6 years, 9 months ago
Don Rumbaoa
Aug 25, 2014

by just looking at the figure and drawing triangles inside the hexagon you will already know how many triangles can be drawn inside it thus knowing the ratio of the triangle AOF to that of the hexagon ABCDEF.

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