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Grade 12th passAlgebra

Number of equilateral triangles in octagon?

Profile image of Chintapalli David Raju
12 Years agoGrade 12th pass
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Profile image of jitender lakhanpal
12 Years ago

hi chintupalli

by octagon u mean to say a regular one i m assuming that a regular octagon of side a

let the number of equilateral triangles be n with one of the side be x

 

so the area covered is root 3 / 4 x2    this should be less than or equal to  the area of octagon 2*a*a*(sqrt(2) + 1)

by the above inequality u will get the number of equilateral triangles depending on the values of x and a