# 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 - Mathematics

MCQ

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

•  ar (ΔABC)

• $\frac{1}{2}$ ar (ΔABC)

• $\frac{1}{3}$ ar (ΔABC)

• $\frac{1}{4}$  ar (ΔABC)

#### Solution

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 =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))

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 19 | Page 62