Each side of an equilateral triangle is 8 cm long. Its area is

Options

A. `32cm^(2)`
B. `64cm^(2)`
C. `16sqrt3cm^(2)`
D. `16sqrt2cm^(2)`

Answer

To find the area of an equilateral triangle with each side measuring 8 cm, we can use the formula for the area of an equilateral triangle:

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

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

### Step-by-Step Solution:

**Step 1: Identify the side length.**
- The side length \( a \) of the equilateral triangle is given as 8 cm.

**Step 2: Substitute the side length into the area formula.**
- We substitute \( a = 8 \) cm into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times (8)^2 \]

**Step 3: Calculate \( (8)^2 \).**
- Calculate \( 8^2 \):
\[ 8^2 = 64 \]

**Step 4: Substitute \( 64 \) back into the area formula.**
- Now substitute \( 64 \) into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 64 \]

**Step 5: Simplify the expression.**
- Simplify \( \frac{64}{4} \):
\[ \frac{64}{4} = 16 \]
- Therefore:
\[ \text{Area} = 16\sqrt{3} \text{ cm}^2 \]

**Final Answer:**
The area of the equilateral triangle is \( 16\sqrt{3} \text{ cm}^2 \).