Find the area and the height of an equilateral triangle whose each side measures :
6.4 m (Take `sqrt(3)=1.73` in each case )

Answer

To find the area and height of an equilateral triangle with each side measuring 6.4 m, we can follow these steps:

### Step 1: Write down the formula for the area of an equilateral triangle.
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:

\[ A = \frac{\sqrt{3}}{4} a^2 \]

### Step 2: Substitute the value of \( a \) into the area formula.
Given that each side \( a = 6.4 \) m, we substitute this value into the formula:

\[ A = \frac{\sqrt{3}}{4} \times (6.4)^2 \]

### Step 3: Calculate \( (6.4)^2 \).
Calculating the square of 6.4:

\[ (6.4)^2 = 40.96 \]

### Step 4: Substitute \( (6.4)^2 \) back into the area formula.
Now we can substitute \( 40.96 \) into the area formula:

\[ A = \frac{\sqrt{3}}{4} \times 40.96 \]

### Step 5: Simplify \( \frac{40.96}{4} \).
Calculating \( \frac{40.96}{4} \):

\[ \frac{40.96}{4} = 10.24 \]

### Step 6: Substitute the value of \( \sqrt{3} \) and calculate the area.
Using \( \sqrt{3} = 1.73 \):

\[ A = 1.73 \times 10.24 \]

### Step 7: Perform the multiplication.
Calculating \( 1.73 \times 10.24 \):

\[ A = 17.7152 \, \text{m}^2 \]

### Step 8: Write down the formula for the height of an equilateral triangle.
The formula for the height \( h \) of an equilateral triangle is given by:

\[ h = \frac{a \cdot \sqrt{3}}{2} \]

### Step 9: Substitute the value of \( a \) into the height formula.
Substituting \( a = 6.4 \) m:

\[ h = \frac{6.4 \cdot \sqrt{3}}{2} \]

### Step 10: Calculate \( \frac{6.4}{2} \).
Calculating \( \frac{6.4}{2} \):

\[ \frac{6.4}{2} = 3.2 \]

### Step 11: Substitute the value of \( \sqrt{3} \) and calculate the height.
Using \( \sqrt{3} = 1.73 \):

\[ h = 3.2 \cdot 1.73 \]

### Step 12: Perform the multiplication.
Calculating \( 3.2 \times 1.73 \):

\[ h = 5.536 \, \text{m} \]

### Final Answer:
- Area of the equilateral triangle: \( 17.7152 \, \text{m}^2 \)
- Height of the equilateral triangle: \( 5.536 \, \text{m} \)