An equilateral triangle has a perimeter of 36 cm. If each side is decreased by 2 cm, by how many square centimeters does the area decrease?

Wed, 06 May 2026 12:28:54 +0000

**An equilateral triangle has a perimeter of 36 cm. If each side is decreased by 2 cm, by how many square centimeters does the area decrease?** Curious about how subtle shape changes impact measurements? A specific question often surfacing in user conversations is: *An equilateral triangle has a perimeter of 36 cm. If each side is decreased by 2 cm, by how many square centimeters does the area decrease?* Beyond a simple geometry problem, this query reflects growing interest in spatial reasoning and real-world applications—from design to education. Understanding these transformations builds a foundation in practical math, useful for learners, professionals, and anyone exploring spatial concepts. True to its precise nature, an equilateral triangle with a perimeter of 36 cm has each side measuring 12 centimeters. Reducing each side by 2 cm results in a new length of 10 cm per edge. While the perimeter drops to 30 cm, the real impact lies in the shift in area—a decrease revealing broader implications for geometry and visual estimation. To calculate this change, begin with the original area. Using the formula for equilateral triangles:
Area = (√3 / 4) × side²
For a 12 cm side:
Area = (√3 / 4) × 144 ≈ 62.35 cm² (approximately)