# What the area of an equilateral triangle if the side length is 6 mm?

We can see that if we split an equilateral triangle in half, we are left with two congruent equilateral triangles. Thus, one of the legs of the triangle is

If we want to determine the area of the entire triangle, we know that

In your case, the area of the triangle is

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The area of an equilateral triangle with side length ( s ) is given by the formula:

[ \text{Area} = \frac{\sqrt{3}}{4} \times s^2 ]

Substituting the given side length ( s = 6 ) mm into the formula:

[ \text{Area} = \frac{\sqrt{3}}{4} \times (6)^2 ]

[ \text{Area} = \frac{\sqrt{3}}{4} \times 36 ]

[ \text{Area} = \frac{\sqrt{3} \times 36}{4} ]

[ \text{Area} = \frac{\sqrt{3} \times 36}{4} ]

[ \text{Area} = \frac{36\sqrt{3}}{4} ]

[ \text{Area} = 9\sqrt{3} ]

So, the area of the equilateral triangle is ( 9\sqrt{3} ) square millimeters.

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