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

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.