समबाहु त्रिभुज ABC का परिमाप 10.2 cm है। त्रिभुज का क्षेत्रफल क्या है?

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  1. \(18.9\sqrt{3} \, \text{cm}^2 \)
  2. \(1.89\sqrt{3} \, \text{cm}^2\)
  3. \(2.89\sqrt{3} \, \text{cm}^2 \)
  4. \(28.9\sqrt{3} \, \text{cm}^2 \)

Answer (Detailed Solution Below)

Option 3 : \(2.89\sqrt{3} \, \text{cm}^2 \)
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दिया गया है:

समबाहु त्रिभुज ABC का परिमाप 10.2 सेमी है।

प्रयुक्त सूत्र:

समबाहु त्रिभुज का क्षेत्रफल = \( \dfrac{\sqrt{3}}{4} \times a^2\)

जहाँ, a = समबाहु त्रिभुज की भुजा की लंबाई

गणना:

समबाहु त्रिभुज का परिमाप = 3a

⇒ 3a = 10.2

⇒ a = 3.4 सेमी

क्षेत्रफल = \(\dfrac{\sqrt{3}}{4} \times (3.4)^2\)

⇒ क्षेत्रफल = \(\dfrac{\sqrt{3}}{4} \times 11.56\)

⇒ क्षेत्रफल = \(2.89\sqrt{3}\) सेमी2

∴ सही उत्तर विकल्प 3 है।

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