Question

3.lengths of adjacent sides of a parallelogram is 3cm and 4cm. find its area?​

Answer 1

$\huge\bold{Answer:-}$

Given :

The two sides of a parellogram are 3 and 4 cm respectively

To Find :

The area of the parallelogram .

Solution:-

As it is a parellelogram so its opposite sides must be equal .

Now ,

let , The side AB and DC of the parellelogram be 3 Cm .

and , The side AD and CB of the parellelogram be 4 Cm.

Construction :-

Draw a diagonal AC through the point A to C of it .

Now,

let, AD be the height and CD be the base

so,

By pythagoras theorem ,

AC ² = AD ² + DC ² ( as AC is the hypotenus )

AC² = ( 4)² + ( 3) ²

AC ² = 16 + 9

AC ² = 25

AC = √25

AC = 5 cm

so, The Area of the ΔADC = $\dfrac{1}{2}$ × base × height sq.unit

= $\dfrac{1}{2}$ × 4 × 3 cm²

= 2 × 3 cm²

= 6 cm²

Now, Area of the parallelogram ABCD = 2 × AREA OF ΔADC

= ( 2 × 6 ) CM²

= 12 CM²

Therefore , The area of the parallelogram ABCD is 12 cm².