Find the area of an equilateral triangle of side 8 cm .

Answer

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

### Step 1: Identify the formula for the area of an equilateral triangle.
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

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

### Step 3: Calculate \( (8)^2 \).
Calculating \( (8)^2 \):
\[ (8)^2 = 64 \]

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

### Step 5: Simplify the expression.
To simplify \( \frac{64}{4} \):
\[ \frac{64}{4} = 16 \]
Thus, we have:
\[ A = 16\sqrt{3} \text{ cm}^2 \]

### Step 6: State the final answer.
The area of the equilateral triangle is:
\[ \boxed{16\sqrt{3} \text{ cm}^2} \]

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