Draw In Some Lines

Geometry Level 1

If the total area of the regular hexagon above is 6, what is the area of the light blue star?

4 5 3 2

1 solution

展豪張
Mar 9, 2016

Cut it and count it!!!

Nice lines. :)

Zandra Vinegar Staff - 5 years, 3 months ago

Thank you :) I draw it by mspaint :P

展豪張 - 5 years, 3 months ago

How is the answer 4. Tried to see the symmetry, but could not see the method which points to the answer as 4. Can u explain?

Ajit Deshpande - 5 years, 3 months ago

You can either count all of the congruent triangles and look at the total ratio, or note that there are 12 symmetric parts of the sectioned-up hexagon, each of which is $\frac{2}{3}$ blue:

Since it's given that the area of the hexagon is 6, the area of the blue star is $\frac{2}{3} \times 6 = 4$ .

Zandra Vinegar Staff - 5 years, 3 months ago

thank you for the explanation.

Ajit Deshpande - 5 years, 3 months ago

Draw In Some Lines

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