Question

In the adjoining figure, ABCD and BEFG are two parallelograms.

Prove that : area (◻ABCD) = area (◻BEFG).

Answer 1

Given:

ABCD and BEFG are two parallelograms. 

They share vertex B and are connected as shown in the figure.

To Prove: area (◻ABCD) = area (◻BEFG).

Proof:

Step 1: Use properties of parallelograms

In any parallelogram, area is given by:

Area = Base × Height

Step 2: Observe base and height  

From the figure:

AB is common to both parallelograms.

Sides AD || BC in ABCD and BG || EF in BEFG

The direction of arrows and construction shows:

AD = BF

DC = EG

Also, both parallelograms are constructed on equal bases and between the same set of parallel lines i.e., they have the same height.

Step 3: Conclude

Since, AB = BE   ...(Equal bases) 

Both parallelograms lie between the same parallel lines equal height

Thus, area (ABCD) = base × height = area (BEFG)

Hence proved.