If the length of the side of an equilateral triangle is 6 cm, what is its area ?

Options

A. `18sqrt(3)` sq. cm
B. `36sqrt(3)` sq. cm
C. `27sqrt(3)` sq. cm
D. `9sqrt(3)` sq. cm

Answer

To find the area of an equilateral triangle with a side length of 6 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 given side length into the formula.
In this case, the side length \( a \) is 6 cm. We substitute this value into the formula:
\[ A = \frac{\sqrt{3}}{4} (6)^2 \]

### Step 3: Calculate \( (6)^2 \).
Calculating \( (6)^2 \) gives us:
\[ (6)^2 = 36 \]

### Step 4: Substitute back into the area formula.
Now we substitute \( 36 \) back into the area formula:
\[ A = \frac{\sqrt{3}}{4} \times 36 \]

### Step 5: Simplify the expression.
Now we simplify the expression:
\[ A = \frac{36\sqrt{3}}{4} \]
Calculating \( \frac{36}{4} \) gives us \( 9 \):
\[ A = 9\sqrt{3} \text{ cm}^2 \]

### Final Answer:
Thus, the area of the equilateral triangle is:
\[ \boxed{9\sqrt{3} \text{ cm}^2} \]

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