Question

What is the area of an equilateral triangle with side length of 4 cm?

• A. $\frac{\sqrt{3}}{4} \text{ cm}^2$
• B. $2\sqrt{3} \text{ cm}^2$
• C. $4\sqrt{3} \text{ cm}^2$
• D. $16\sqrt{3} \text{ cm}^2$

Answer 1

Answer:

$4\sqrt{3} \text{ cm}^2$

The correct answer is Option C ($4\sqrt{3} \text{ cm}^2$).

To find the area of an equilateral triangle, we use a specific formula that depends only on the length of its side ($a$).

Step-by-Step Calculation

1. Identify the Formula:
   The area ($A$) of an equilateral triangle is given by:
   $A = \frac{\sqrt{3}}{4} a^2$

2. Substitute the Given Side ($a = 4$):
   $A = \frac{\sqrt{3}}{4} \times (4)^2$

3. Simplify:
   $A = \frac{\sqrt{3}}{4} \times 16$

4. $A = 4\sqrt{3} \text{ cm}^2$