The area of the equilateral triangle whose side is 8 cm is:

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64 c m^{2}

16 \sqrt 3 c m^{2}

21.3 c m^{2}

4 \sqrt 3 c m^{2}

answer is B.

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Detailed Solution

Concept- Here, a stands for each side's length and A for area.
Here, we are given the equilateral triangle's side, and we must determine its area. Here, understanding what an equilateral triangle is necessary. The triangle whose lengths on each of its three sides equals 8 cm is the one being discussed here.
The equilateral triangle in question has a side of 8 cm.

Here, all three sides of the triangle are equal to 8 cm, so we need to know how to compute the area of the equilateral triangle.
Area(A)=

\frac{\sqrt 3}{4} a^{2}

Here, a stands for each side's length and A for area.
Therefore, we can state that a=8cm.
In the formula for the area of an equilateral triangle, we get the following result when we substitute the value of a=8:
Area(A) =

\frac{\sqrt 3}{4} a^{2}

, A =

\frac{\sqrt 3}{4} 8^{2}

, and A =

\frac{\sqrt 3}{4} \times 64

=16

\sqrt

3
In this case, the area is valued at 16

\sqrt

3, and the formula predicts that its units are as follows:
Since we used the square of the side in the formula, the unit of area will be the square of the side, which is denoted by centimetre=cm.
So, A=