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 (Δ

*ABC*)- \[\frac{1}{2}\] ar (Δ
*ABC*) - \[\frac{1}{3}\] ar (Δ
*ABC*) - \[\frac{1}{4}\] ar (Δ
*ABC*)

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#### 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)) `

Concept: Concept of Area

Is there an error in this question or solution?

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