Find the area of an equilateral triangle whose sides are 12 cm.

Options

A. a)`29 sqrt5`
B. b)`45 sqrt2`
C. c)38
D. d)`36 sqrt3`

Answer

To find the area of an equilateral triangle with a side length of 12 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 side length into the formula.
Given that the side length \( A \) is 12 cm, 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 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.
Now, simplify \( \frac{144}{4} \):

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

So, we have:

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

### Step 6: Final result.
Thus, the area of the equilateral triangle is:

\[ A = 36\sqrt{3} \text{ cm}^2 \]