Question

The area of an equilateral triangle with sides of length \( \alpha \) is

• A. \( \frac{\sqrt{3}}{4} \alpha^2 \)
• B. \( \frac{\sqrt{3}}{2} \alpha^2 \)
• C. \( \frac{1}{2} \alpha^2 \)
• D. \( \frac{1}{\sqrt{2}} \alpha^2 \)

Hint:

The area of an equilateral triangle can be calculated using the formula \( \frac{\sqrt{3}}{4} a^2 \), where \( a \) is the length of the side.

Answer 1

The Correct Option is A

Step 1: Formula for the area of an equilateral triangle.
The area \( A \) of an equilateral triangle is given by the formula: \[ A = \frac{\sqrt{3}}{4} a^2 \] where \( a \) is the side length of the triangle.

Step 2: Substituting the side length.
In this case, the side length is \( \alpha \), so the area becomes: \[ A = \frac{\sqrt{3}}{4} \alpha^2 \]

Step 3: Conclusion.
The correct answer is (A) \( \frac{\sqrt{3}}{4} \alpha^2 \).