Question
Download Solution PDFΔABC चे क्षेत्रफळ 63 चौ. एकक आहे. DE, FG दोन समांतर रेषा अशा प्रकारे काढल्या आहेत की त्या रेषाखंड AB आणि AC ला तीन समान भागात विभागतात. चतुर्भुज DEGF चे क्षेत्रफळ किती आहे?
A. 28 चौ. एकक
B. 35 चौ. एकक
C. 21 चौ. एकक
D. 48 चौ. एकक
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAD = DF = FB = x एकक आणि AE = EG = GC = y एकक असे मानू
प्रश्नानुसार,
⇒ ΔADE चे क्षेत्रफळ/ΔABC चे क्षेत्रफळ = (AD/AB)2
⇒ ΔADE चे क्षेत्रफळ/63 = (x/3x)2
⇒ ΔADE चे क्षेत्रफळ = 63 × 1/9
⇒ ΔADE चे क्षेत्रफळ = 7
प्रश्नानुसार,
⇒ ΔAFG चे क्षेत्रफळ/ΔABC चे क्षेत्रफळ = (AF/AB)2
⇒ ΔAFG चे क्षेत्रफळ/63 = (2x/3x)2
⇒ ΔAFG चे क्षेत्रफळ = 63 × 4/9
⇒ ΔAFG चे क्षेत्रफळ = 28
∴ चतुर्भुज DEGF चे क्षेत्रफळ = (ΔAFG - ΔADE) चे क्षेत्रफळ = (28 - 7) = 21 चौ. एकक
Last updated on Jul 2, 2025
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