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 ______.

Options

• `1/2` ar (ABC)

• `1/3` ar (ABC)
• `1/4` ar (ABC)
• ar (ABC)

Answer 1

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 `underlinebb(1/2 ar  (ABC))`.

Explanation:

Given: ABCD is a triangle.

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 = `1/2 BC xx 1/2 AE`  ...(E is the midpoint of BC)

area of || ^gm DECF = `1/2(1/2BC xx AE)`

area of || ^gm DECF = `1/2(ar ( ΔABC) `