Question

In Triangle ABC; D, E, F are the midpoints of BC, CA, AB. BE and DF intersects at the point G. What is the area of the quadrilateral AFGE if ABC has the area of 512?

Answer 1

Answer:

Correct option is

A

51

If R, Q and P are the midpoints of AB, AC and BC, and by applying the theorem:-

The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get

PQ=

2

1

AB=AR and PQ∣∣AR

PQ=

2

1

AC=AQ and PR∣∣AQ

Since the above conditions are sufficient for a parallelogram, therefore ARPQ is a parallelogram.

∴ Perimeter of ∥

gm

=ARPQ=2(AR+AQ)=AB+AC=(30+21)cm=51cm