Question
Download Solution PDFఒక వృత్తంలో ఉన్న ఒక చతురస్రం మరియు ఒక సాధారణ షడ్భుజి యొక్క వైశాల్యం యొక్క నిష్పత్తి కనుగొనండి?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFపై రేఖాచిత్రంలో, వృత్తం యొక్క వ్యాసం చతురస్రం యొక్క కర్ణం యొక్క పొడవుకు సమానంగా ఉంటుంది.
⇒ √2a = 2r
⇒ a = √2r
⇒ చతురస్రం యొక్క వైశాల్యం = a2 = (√2r)2 = 2r2
పై రేఖాచిత్రంలో, వృత్తం యొక్క వ్యాసార్థం షడ్భుజి భుజంకు సమానంగా ఉంటుంది.
షడ్భుజి 6 సమబాహు త్రిభుజాలను కలిగి ఉంటుంది,
⇒ షడ్భుజి వైశాల్యం = 6 × √3/4 × a2 = 6 × √3/4 × r2
∴ చతురస్రం మరియు షడ్భుజి వైశాల్యాల నిష్పత్తి = 2r2 : 6 × √3/4 × r2 = 4 : 3√3Last updated on Jun 11, 2025
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