Question

The area of a triangle ABC 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​

Answer 1

$\huge{\text{\underline{Question:-}}}$

The area of a triangle ABC 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?

$\huge{\text{\underline{Answer:-}}}$

Area of quadrilateral DEFG ⟹ 21 sq.units.

$\huge{\text{\underline{Explaination:-}}}$

$\bigstar$Point to remember:-

• Area of a triangle is proportional to square of the sides.

• Point D and F divides the line AB into 3 equal parts AD, DF and FB

⟹ AD/AB = 1/3

⟹ AF/AB = 2/3

Considering similar triangles, ΔADE and ΔABC

Area of ΔADE/Area of ΔABC = AD²/AB²

⟹ Area of ΔADE/63 = 1/9

⟹ Area of ΔADE = 63/9 = 7

Similarly considering similar triangles ΔAFG and ΔABC

Area of ΔAFG/Area of ΔABC = AF²/AB²

⟹ Area of ΔAFG/63 = 4/9

⟹ Area of ΔAFG = 63 x 4/9

$\large{\boxed{\text{= 28}}}$

Area of quadrilateral DEFG = Area of ΔAFG - Area of ΔADE

= 28 - 7

$\large{\boxed{\text{= 21 sq.units}}}$

Hence option C) 21sq. units is the correct answer.

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