Find the area of an equilateral triangle each of whose sides measures (1) 18 cm, (11) 20 cm.`[Take sqrt3 = 1.73]`

Answer

To find the area of an equilateral triangle, we can use the formula:

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

where \(\sqrt{3}\) is given as 1.73.

### Step 1: Calculate the area for the first triangle with side 18 cm.

1. **Identify the side length**: The side length of the triangle is 18 cm.
2. **Square the side length**:
\[ \text{side}^2 = 18^2 = 324 \text{ cm}^2 \]
3. **Substitute into the area formula**:
\[ \text{Area} = \frac{1.73}{4} \times 324 \]
4. **Calculate \(\frac{1.73}{4}\)**:
\[ \frac{1.73}{4} = 0.4325 \]
5. **Multiply by 324**:
\[ \text{Area} = 0.4325 \times 324 = 140.13 \text{ cm}^2 \]

### Step 2: Calculate the area for the second triangle with side 20 cm.

1. **Identify the side length**: The side length of the triangle is 20 cm.
2. **Square the side length**:
\[ \text{side}^2 = 20^2 = 400 \text{ cm}^2 \]
3. **Substitute into the area formula**:
\[ \text{Area} = \frac{1.73}{4} \times 400 \]
4. **Calculate \(\frac{1.73}{4}\)**:
\[ \frac{1.73}{4} = 0.4325 \]
5. **Multiply by 400**:
\[ \text{Area} = 0.4325 \times 400 = 173 \text{ cm}^2 \]

### Final Results:
- The area of the equilateral triangle with side 18 cm is **140.13 cm²**.
- The area of the equilateral triangle with side 20 cm is **173 cm²**.