What is the area of an equilateral triangle of side 16 cm?

Options

A. `48sqrt3` Sq. cm
B. `128sqrt3` Sq. cm
C. `9.6sqrt3` Sq. cm
D. `64sqrt3` Sq. cm

Answer

To find the area of an equilateral triangle with a side length of 16 cm, we can use the formula for the area of an equilateral triangle:

\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]

where \( a \) is the length of a side of the triangle.

### Step 1: Identify the side length
Given:
- Side length \( a = 16 \) cm

### Step 2: Substitute the side length into the formula
Substituting \( a \) into the area formula:

\[ \text{Area} = \frac{\sqrt{3}}{4} (16)^2 \]

### Step 3: Calculate \( (16)^2 \)
Calculating \( (16)^2 \):

\[ (16)^2 = 256 \]

### Step 4: Substitute back into the area formula
Now substitute \( 256 \) back into the area formula:

\[ \text{Area} = \frac{\sqrt{3}}{4} \times 256 \]

### Step 5: Simplify the expression
Now simplify \( \frac{256}{4} \):

\[ \frac{256}{4} = 64 \]

So, the area becomes:

\[ \text{Area} = 64\sqrt{3} \, \text{cm}^2 \]

### Final Answer
Thus, the area of the equilateral triangle is:

\[ 64\sqrt{3} \, \text{cm}^2 \]