Equilateral triangle perimeter 90 cm — find area: An equilateral triangle has perimeter 90 cm. Find its area (in sq cm).

Introduction / Context:
For equilateral triangles, perimeter directly gives the side, and area follows from the standard formula in one step.

Given Data / Assumptions:
Perimeter = 90 cm → side a = 90/3 = 30 cm.

Concept / Approach:
Area A = (sqrt(3)/4) * a^2 = (sqrt(3)/4) * 30^2.

Step-by-Step Solution:
A = (sqrt(3)/4) * 900 = 225*sqrt(3) sq cm

Verification / Alternative check:
Units consistent; formula is standard for equilateral triangles.

Why Other Options Are Wrong:
They stem from mis-squaring the side or misapplying the 1/4 factor.

Common Pitfalls:
Using 30*sqrt(3) instead of (sqrt(3)/4)*900.

Final Answer:
225√3 sq cm