Question

If \( L_1 \) and \( L_2 \) are two parallel lines and \( \triangle ABC \) is an equilateral triangle, then the area of triangle ABC is

• A. \( 7\sqrt{3} \)
• B. \( 4\sqrt{3} \)
• C. \( 21\sqrt{3} \)
• D. 84

Hint:

For equilateral triangles, use the formula \( \frac{\sqrt{3}}{4} s^2 \) to calculate the area directly when given the side length.

Answer 1

The Correct Option is C

Step 1: Understand the geometry of the triangle.
In this problem, we are dealing with an equilateral triangle with side length \( 6 \), and the height is given as \( 3 \). The area of an equilateral triangle can be calculated using the formula: \[ \text{Area} = \frac{\sqrt{3}}{4} s^2 \] where \( s \) is the side length of the triangle. Step 2: Apply the formula for the area of the equilateral triangle.
Substitute \( s = 6 \) into the formula: \[ \text{Area} = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \] This gives the area of triangle \( ABC \) as \( 21\sqrt{3} \). \includegraphics[width=0.5\linewidth]{5(4).png}