The area of an equilateral triangle of side 20 cm is

Options

A. `100/(sqrt3) cm^2`
B. `100sqrt(3) cm^2`
C. `100 (sqrt3)/2 cm^2`
D. `100 (sqrt3)/(4) cm^2`

Answer

To find the area of an equilateral triangle with a side length of 20 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:

1. **Identify the side length**:
The side length \( a \) of the equilateral triangle is given as 20 cm.

2. **Substitute the side length into the area formula**:
We substitute \( a = 20 \) cm into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times (20)^2 \]

3. **Calculate \( (20)^2 \)**:
First, we calculate the square of the side length:
\[ (20)^2 = 400 \]

4. **Multiply by \( \frac{\sqrt{3}}{4} \)**:
Now we substitute \( 400 \) back into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 400 \]

5. **Simplify the expression**:
We can simplify \( \frac{400}{4} \):
\[ \frac{400}{4} = 100 \]
Therefore, the area becomes:
\[ \text{Area} = 100\sqrt{3} \text{ cm}^2 \]

### Final Answer:
The area of the equilateral triangle is \( 100\sqrt{3} \) cm².