Find the area of an equilateral triangle with a side length of 12

Options

A. `6sqrt3`
B. `18sqrt3`
C. `36sqrt3`
D. `72sqrt3`

Answer

To find the area of an equilateral triangle with a side length of 12, 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 side length into the formula.
Here, the side length \( a \) is 12. We substitute this value into the formula:

\[ A = \frac{\sqrt{3}}{4} (12)^2 \]

### Step 3: Calculate \( 12^2 \).
Calculating \( 12^2 \):

\[ 12^2 = 144 \]

### Step 4: Substitute \( 144 \) back into the area formula.
Now, substitute \( 144 \) back into the area formula:

\[ A = \frac{\sqrt{3}}{4} \times 144 \]

### Step 5: Simplify the expression.
Next, we simplify \( \frac{144}{4} \):

\[ \frac{144}{4} = 36 \]

So now we have:

\[ A = 36\sqrt{3} \]

### Step 6: State the final answer.
Thus, the area of the equilateral triangle with a side length of 12 is:

\[ A = 36\sqrt{3} \text{ square units} \]

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