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In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is (√3 = 1732)
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- 98.55 sq cm
- 100 sq cm
- 101 sq cm
- 95 sq cm
- 98.55 sq cm
Correct Option: A
Using Rule 18, 6 and 14,
| In-radius = | ||
| 2√3 |
| = | = 4√3 cm | |
| 2√3 |
| Arae of triangle = | × (side)² | |
| 4 |
| = | × 24 × 24 | |
| 4 |
= 144√3 sq.cm.
= 144 × 1.732 = 249.408 sq.cm.
Area of circle = πr²
| = | × 4√3 × 4√3 | |
| 7 |
| = | = 150.86 sq.cm. | |
| 7 |
Area of remaining part = (249.408 – 150.86) sq.cm.
= 98.548 sq.cm.
≈ 98.55 sq.cm.
