A rabbit is tied to one end of an equilateral triangle of side 5 m with a rope…

Standard convention for this class of placement-exam problem: the rope itself is treated as unobstructed by the field (only the animal's own body may not enter it), so the region that is genuinely off-limits is exactly the field's own footprint. The maximum grazing area is therefore taken as the area of the full circle of radius equal to the rope length, centered at the tied vertex, minus the area of the field itself.

1. Circle area with radius equal to the rope length: π × 8² = 64π ≈ 201.06 m².

2. Area of the equilateral triangular field itself (side 5 m): (√3/4) × 5² = 25√3/4 ≈ 10.83 m² — this is the only region the rabbit cannot enter.

3. Maximum area the rabbit can cover = circle area − triangle area = 201.06 − 10.83 ≈ 190.24 m².

Cross-check: the rope (8 m) is longer than the triangle's side (5 m), but the triangle's own footprint is small next to the radius-8 m circle, so the result (190.24 m²) stays only slightly below the full circle's 201.06 m² — consistent with only a small region being blocked off.