The height of an equilateral triangle is 10 cm. Its area is

Options

A. `(100)/(3) cm^(2)`
B. 30 `cm^(2)`
C. 100 `cm^(2)`
D. `(100)/(sqrt(3)) cm^(2)`

Answer

To find the area of an equilateral triangle when the height is given, we can use the formula:

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

where \( h \) is the height of the triangle.

### Step-by-Step Solution:

1. **Identify the height of the triangle**:
The height \( h \) of the equilateral triangle is given as 10 cm.

2. **Substitute the height into the area formula**:
\[ \text{Area} = \frac{h^2}{\sqrt{3}} = \frac{10^2}{\sqrt{3}} \]

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

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

5. **Final expression for the area**:
The area of the equilateral triangle is:
\[ \text{Area} = \frac{100}{\sqrt{3}} \, \text{cm}^2 \]