-
The area of the incircle of an equilateral triangle of side 42 cm
is (Take π = 22/7) :
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- 231 cm²
- 462cm²
- 22√3 cm²
- 924 cm²
- 231 cm²
Correct Option: B
Let ABC be the equilateral triangle of side 42 cm and let AD be perpendicular from A on BC.
Since the triangle is equilateral, so D bisects BC.
∴ BD = CD = 21 cm.
The centre of the inscribed circle will coincide with the centroid of ∆ ABC.
| Therefore, OD = | AD | |
| 3 |
In ∆ ABC
AB² = AD² + BD²
→ 42² = AD² + 21²
⇒ AD = √42² – 21²
= √(42 + 21)(42 - 21)
= √63 × 21 = 3 × 7√3cm
| ∴ OD = | AD = × 7√3 | |
| 3 |
| = | × 7√3× 7√3 | |
| 7 |
= 22 × 7 × 3 = 462 cm²
