Question
Download Solution PDF△ABC-তে, MN∥BC, চতুর্ভুজ MBCN-এর ক্ষেত্রফল = 130 সেমি2। যদি AN : NC = 4 : 5 হয়, তাহলে △MAN-এর ক্ষেত্রফল কত?
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Detailed Solution
Download Solution PDFপ্রদত্ত,
চতুর্ভুজ MBCN-এর ক্ষেত্রফল = 130 সেমি2.
AN : NC = 4 : 5
অতএব, AC = 4 + 5 = 9
△ABC-তে, যদি MN∥BC হয়, তাহলে
△AMN-এর ক্ষেত্রফল/△ABC-এর ক্ষেত্রফল = (AN/AC)2
△AMN-এর ক্ষেত্রফল/△ABC-এর ক্ষেত্রফল = (4/9)2 = 16/81
△AMN-এর ক্ষেত্রফল = 16 একক এবং △ABC-এর ক্ষেত্রফল = 81 একক
এখন, চতুর্ভুজ MBCN-এর ক্ষেত্রফল = △ABC-এর ক্ষেত্রফল - △AMN-এর ক্ষেত্রফল
⇒ 81 - 16 একক = 130 সেমি2
⇒ 65 একক = 130 সেমি2
⇒ 1 একক = 130/65 = 2 সেমি2
∴ △AMN-এর ক্ষেত্রফল = 16 × 2 = 32 সেমি2Last updated on Jun 13, 2025
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