Area of an equilateral triangle = $25\sqrt{3} \text{ cm}^2$

Remember that for an equilateral triangle, if Area = $k\sqrt{3}$, then side $a = \sqrt{4k}$. Here $k=25$, so $a = \sqrt{4 \times 25} = \sqrt{100} = 10$. Perimeter is $3 \times 10 = 30$.

Confusing the area formula for an equilateral triangle with other triangles or forgetting to multiply the side by 3 to get the perimeter.

This formula relates closely to coordinate geometry where you might need the height ($h = \frac{\sqrt{3}}{2}a$) or the area given coordinates of vertices.