Six regular hexagons surround a regular hexagon of side length 1 as shown.What is the area of triangle ABC?

Question

tinash · Answer

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jhonyy9 · Answer

so than you see it right the triangle ABC is an equailateral triangle - with angle measure 60 degree  - 
- every angle A,B and C has bisected by one side of a hexagon so in two agles with 30 and 30 degree |dw:1456962445445:dw|

jhonyy9 · Answer

so now than we have got the length of FE and we know the length of hypotenuse so we can calcule easy using pythagora s theorem the length of BF ,what is a quarter part of a side of this equilateral triangle 

BF^2 = 1 - 1/4 

BF = sqrt(3/4) 

BF = sqrt3 / 2   - so because this is a quarter part of a side length of triangle so just multiplie it by 4 and will get the length of a side of equilateral triangle

AB = 4*sqrt3 / 2 = 2sqrt3

AB = BC = AC = 2sqrt3 

area of this equilateral triangle we can calcule than we know the height of this triangle 

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