A very simple and easy probem

The area of a triangle can be described as

$\frac{1}{2}$ a b sin C

where a and b stands for side lengths of the triangle, and C stands for the angle between the two line segments a and b.

An equilateral triangle has an interior angle of 60, and equal side lengths.

Therefore, a = b = c .

Given that the area is $10cm^{2}$ , we can form the equation

$\frac{1}{2}$ a a sin 60 = 10

a = 4.80562

The area of an equilateral triangle is given by $A=\dfrac{\sqrt{3}}{4}x^2$ where $x$ is the side length. So we have

$10=\dfrac{\sqrt{3}}{4}x^2$

$x^2=\dfrac{40}{\sqrt{3}}$

$x=\sqrt{\dfrac{40}{\sqrt{3}}}\approx \boxed{4.80562 ~cm}$

Area of an equilateral triangle is $\dfrac{ \sqrt{3}}{4}a^2$

Given $\dfrac{ \sqrt{3}}{4}a^2=10cm^2$ $\dfrac{ \sqrt{40}}{\sqrt{\sqrt{3}}}=a$ $a=\dfrac{6.32455}{1.31607}$ $a=4.80562$