Question
Download Solution PDFΔABC में, MN∥BC, चतुर्भुज MBCN का क्षेत्रफल = 130 सेमी2। यदि AN : NC = 4 : 5, तो ΔMAN का क्षेत्रफल है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है,
चतुर्भुज MBCN का क्षेत्रफल = 130 सेमी2.
AN : NC = 4 : 5
अतः, AC = 4 + 5 = 9
ΔABC में, यदि MN∥BC, तो
ΔAMN का क्षेत्रफल/ΔABC का क्षेत्रफल = (AN/AC)2
ΔAMN का क्षेत्रफल/ΔABC का क्षेत्रफल = (4/9)2 = 16/81
ΔAMN का क्षेत्रफल = 16 इकाई और ΔABC का क्षेत्रफल = 81 इकाई
अब, चतुर्भुज MBCN का क्षेत्रफल = ΔABC का क्षेत्रफल - ΔAMN का क्षेत्रफल
⇒ 81 - 16 इकाई = 130 सेमी2
⇒ 65 इकाई = 130 सेमी2
⇒ 1 इकाई = 130/65 = 2 सेमी2
∴ ΔAMN का क्षेत्रफल = 16 × 2 = 32 सेमी2
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