Question

PQRS and EFRS are two parallelogram then are (MFR)=ar½(PQRS)

Answer 1

Area (∆ MFR) = ½ * Area (parallelogram PQRS)  

Step-by-step explanation:

Given:

PQRS & EFRS is a parallelogram

To prove: area (MFR)=½ * area (PQRS).

 

Solution:

Step 1:

From figure attache below, we can say that

Both the parallelogram PQRS and EFRS are on the same base SR and lie between the same parallel lines SR and PF.

We know that if two parallelograms are on the same base and lie between the same parallel lines, then they have the same area.

∴ Area (parallelogram PQRS) = Area (parallelogram EFRS) …. (i)

Step 2:

From the given figure, we can say that  

The ΔMFR and the parallelogram EFRS have the same base FR and lie between the same parallel lines EF and SR.

We know that if a triangle and a parallelogram are on the same base and lie between the same parallel lines, then the area of the triangle is equal to half the area of the parallelogram.

∴ Area (∆ MFR) = ½ * Area (parallelogram EFRS) ……. (ii)

Thus,

From (i) & (ii), we get

Area (∆ MFR) = ½ * Area (parallelogram PQRS)

Hence proved

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