Equilateral triangle (side 24 cm) with an inscribed circle: Find the area of the triangle’s region that is outside the circle but inside the triangle (in cm²).

Introduction / Context:The “remaining portion” means triangle area minus the area of the incircle. For an equilateral triangle, the inradius has a simple formula in terms of side length, which makes computation straightforward and exact in radicals; the options here are rounded decimal values.

Given Data / Assumptions:

• Equilateral triangle side a = 24 cm.
• Inradius r = a√3/6.
• Triangle area = (√3/4)a^2.

Concept / Approach:Compute the triangle’s area and the incircle’s area, then subtract. Use either π = 22/7 or π ≈ 3.1416 for the circle; the rounded answer must match given options. Using standard exact expressions first helps consistency.

Step-by-Step Solution:

Verification / Alternative check:Using π = 22/7 gives 48*(22/7) ≈ 150.86, still leading to ~98.55 cm². The closest option is 98.5 sq. cm.

Why Other Options Are Wrong:36.6, 54.2, 72.8 are far from the precise subtraction.

Common Pitfalls:Mistaking circumradius for inradius; forgetting that incircle area uses r, not R.

Final Answer:98.5 sq. cm