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Maths problem

An equilateral triangle and a regular hexagon have the same perimeter. What is the ratio of their areas?

Thnku vv much for any help :smile:


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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by ah4p
An equilateral triangle and a regular hexagon have the same perimeter. What is the ratio of their areas?

Thnku vv much for any help :smile:


Posted from TSR Mobile


if the side of the hexagon is x, what is the side of the equilateral triangle?

do you know the area of a triangle is 1/2 a b sinC?
Reply 2
Avatar for ah4p
ah4p
OP
16
Ah ok thnx so much
So I got 1:4


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Reply 3
Avatar for Simba
Simba
16
Hi ah4p,

1:4 is an incorrect answer, and also you don't need to know that area = 0.5absinC.

Instead, consider splitting the hexagon up into six equilateral triangles, and split the equilaterial triangle you began with into four smaller equilateral triangles (each of which will be the same size as the triangles you split the hexagon into).

This should give you the answer just by inspection and is a much nicer method than employing algebra/trig.

Hope this helps,

Simba
Original post by Simba
...


Good to see you.

:wavey:
(edited 9 years ago)

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