2022 · Q94
In an equilateral triangle of side 2√3 cm, a circle is inscribed touching the sides. What is the area of the remaining portion of the triangle?
Elementary MathematicsCircles
- A(2√3 - π) square cm
- B(3√3 - π) square cm
- C(4√3 - 2π) square cm
- D(4√3 - π) square cm
Explanation
Triangle area = (√3/4)·12 = 3√3; inradius = 2√3·√3/6 = 1, so incircle area = π; remaining = 3√3−π sq cm. For an equilateral triangle, inradius = side×√3/6. The keyed option is B.