Question

The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to

(a) ar (ΔABC)

(b) $\frac{1}{2}$ar (ΔABC)

(c) $\frac{1}{3}$ar (ΔABC)

(d) $\frac{1}{4}$ar (ΔABC)

Answer 1

Given: (1) ABCD is a triangle.

(2) mid points of the sides of ΔABC with any of the vertices forms a parallelogram.

To find: Area of the parallelogram

Calculation: We know that: Area of a parallelogram = base × height

Hence area of ||^gm DECF = EC × EG

area of ||^gm DECF = EC × EG

area of ||^gm DECF = (E is the midpoint of BC)

area of ||^gm DECF =

area of ||^gm DECF =

Hence the result is option (b).