If the length of the side of an equilateral triangle is 8 cm, what is its area ?

Options

A. `32sqrt(3)` sq. cm
B. 16 sq. cm
C. `16sqrt(3)` sq. cm
D. 32 sq. cm

Answer

To find the area of an equilateral triangle with a side length of 8 cm, we can follow these steps:

### Step-by-step Solution:

1. **Identify the formula for the area of an equilateral triangle**:
The area \( A \) of an equilateral triangle can be calculated using the formula:
\[ A = \frac{\sqrt{3}}{4} \times s^2 \]
where \( s \) is the length of a side of the triangle.

2. **Substitute the given side length into the formula**:
Here, the side length \( s \) is given as 8 cm. We substitute this value into the formula:
\[ A = \frac{\sqrt{3}}{4} \times (8)^2 \]

3. **Calculate the square of the side length**:
First, we calculate \( (8)^2 \):
\[ (8)^2 = 64 \]

4. **Substitute the squared value back into the area formula**:
Now we substitute \( 64 \) back into the area formula:
\[ A = \frac{\sqrt{3}}{4} \times 64 \]

5. **Simplify the expression**:
Next, we simplify \( \frac{64}{4} \):
\[ \frac{64}{4} = 16 \]
So, we have:
\[ A = 16\sqrt{3} \]

6. **Write the final answer**:
Therefore, the area of the equilateral triangle is:
\[ A = 16\sqrt{3} \text{ cm}^2 \]