The side of an equilateral triangle is 10 cm. Find its area (in `cm^(2)`).

Options

A. `25sqrt(3)`
B. `36sqrt(3)`
C. `25sqrt(2)`
D. `36sqrt(2)`

Answer

To find the area of an equilateral triangle with a side length of 10 cm, we can use the formula for the area of an equilateral triangle:

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

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

### Step-by-Step Solution:

1. **Identify the side length**:
The side length \( s \) of the equilateral triangle is given as 10 cm.

2. **Substitute the side length into the formula**:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times (10)^2 \]

3. **Calculate \( (10)^2 \)**:
\[ (10)^2 = 100 \]

4. **Substitute back into the area formula**:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 100 \]

5. **Simplify the expression**:
\[ \text{Area} = \frac{100\sqrt{3}}{4} \]
\[ \text{Area} = 25\sqrt{3} \]

6. **Final result**:
The area of the equilateral triangle is \( 25\sqrt{3} \) cm².