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 segments AB and AC into three equal parts. What is the area of the quadrilateral DEFG?

Answer 1

Answer:

Area of quadrilateral DEFG will be 21 sq.units

Step-by-step explanation:

We know that 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    and 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 = 63x4/9 = 28

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

= 28 - 7

= 21 sq.units