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The area of ΔABC is 63 sq. units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF? A. 28 sq. units B. 35 sq. units C. 21 sq. units D. 48 sq. units

The area of ΔABC is 63 sq. units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF? A. 28 sq. units B. 35 sq. units C. 21 sq. units D. 48 sq. units Correct Answer C

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Let, AD = DF = FB = x units and AE = EG = GC = y units

According to the question,

⇒ Area of ΔADE/Area of ΔABC = (AD/AB)2

⇒ Area of ΔADE/63 = (x/3x)2

⇒ Area of ΔADE = 63 × 1/9

⇒ Area of ΔADE = 7

According to the question,

⇒ Area of ΔAFG/Area of ΔABC = (AF/AB)2

⇒ Area of ΔAFG/63 = (2x/3x)2

⇒ Area of ΔAFG = 63 × 4/9

⇒ Area of ΔAFG = 28

∴ Area of the quadrilateral DEGF = Area of (ΔAFG - ΔADE) = (28 - 7) = 21 sq. units

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