What is the area (in cm²) of an equilateral triangle whose side length is 14 cm? Use the standard area formula for equilateral triangles in terms of their side.

Introduction:
Equilateral triangles are special triangles whose three sides and three angles are all equal. There is a direct formula for their area in terms of the side length, which avoids computing the height separately. This problem checks your ability to apply that formula correctly.

Given Data / Assumptions:

• The triangle is equilateral.
• Each side has length 14 cm.
• We must compute its area in square centimetres.

Concept / Approach:
For an equilateral triangle with side length a, the area A is given by: A = (√3 / 4) * a². This comes from deriving the height using Pythagoras in a 30°–60°–90° triangle inside the equilateral triangle, then substituting into the general area formula (1/2 * base * height).

Step-by-Step Solution:
Given side length a = 14 cm. Use the formula A = (√3 / 4) * a². Compute a² = 14² = 196. Substitute: A = (√3 / 4) * 196. Simplify 196 / 4 = 49. Thus A = 49√3 cm².

Verification / Alternative check:
Alternatively, compute the height h first. For an equilateral triangle, h = (√3 / 2) * a = (√3 / 2) * 14 = 7√3. Then area A = (1/2) * base * height = (1/2) * 14 * 7√3 = 7 * 7√3 = 49√3 cm², which matches the formula based result.

Why Other Options Are Wrong:
Options (49/2)√3, (49/4)√3, and 98√3 result from misplacing the factor of 1/4 or incorrectly handling the square of 14. The area must scale with the square of the side, so doubling the side more than quadruples the area. Only 49√3 cm² is consistent with the correct formula and computations.

Common Pitfalls:
Learners sometimes forget to square the side or misapply the coefficient, using √3/2 instead of √3/4 in the area formula. Others confuse height and side. Keeping the formula A = (√3 / 4) * a² clearly in mind prevents such errors.

Final Answer:
The area of the equilateral triangle is 49√3 cm².