Each side of an equilateral triangle is 8 cm. Its area is

Options

A. `16sqrt3 cm^(2)`
B. `32sqrt3 cm^(2)`
C. `24sqrt3 cm^(2)`
D. `8sqrt3 cm^(2)`

Answer

To find the area of an equilateral triangle with each side measuring 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:
\[ A = \frac{\sqrt{3}}{4} a^2 \]
where \( a \) is the length of a side of the triangle.

2. **Substitute the value of the side into the formula**:
Given that each side \( a = 8 \) cm, we substitute this value into the formula:
\[ A = \frac{\sqrt{3}}{4} \times (8)^2 \]

3. **Calculate \( (8)^2 \)**:
First, calculate the square of 8:
\[ (8)^2 = 64 \]
Now substitute this back into the area formula:
\[ A = \frac{\sqrt{3}}{4} \times 64 \]

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

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