The side of an equilateral triangle is 8cm. Find its area (in `cm^(2)`).

Options

A. `25sqrt(3)`
B. `16sqrt(2)`
C. `25sqrt(2)`
D. `16sqrt(3)`

Answer

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

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

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

### 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.
Now simplify the expression:
\[ A = \frac{64\sqrt{3}}{4} \]
\[ A = 16\sqrt{3} \]

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

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