# Find the length of the side of equilateral triangle of area 10.2 m^2?

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We'll recall the following formula that gives the area of a triangle:

A = side*side*sine of the angle included/2

Since the lengths of the sides of an equilateral triangle are equal, let the length of the side be x.

A = `x^(2)` * sin 60/2

10.2 = `x^(2)` *`sqrt(3)` /4

40.8 = `sqrt(3)` `x^(2)`

x = `sqrt(40.8/sqrt(3))` m

x = 4.853 m

**Therefore, the requested length of the side of equilateral triangle is x = 4.853 m.**