Question

the adjacent sides of parallelogram are 6cm and 4cm.if the height corresponding to longer side is 3cm.find the area of parallelogram and the height corresponding to the shorter side​

Answer 1

Answer:

• Area of parallelogram is 18 cm².
• Height corresponding to shorter side is 4.5 cm.

Step-by-step explanation:

Given:-

• Adjacent sides of parallelogram are 6 cm and 4 cm.
• Height corresponding to longer side is 3cm.

To find:-

• Area of parallelogram.
• Height corresponding to the shorter side.

Solution:-

We know,

Opposite sides of parallelogram are equal.

So,

Longer side of parallelogram is 6 cm because opposite side of 6 cm is 6 cm.

And similarly, Opposite side of 4 cm is 4 cm.

Thus, 6 cm is longer side of parallelogram.

And, 4 cm is shorter side of parallelogram.

Height corresponding to 6 cm is 3 cm.

Area of parallelogram = Base×Height.

Base = 6 cm

Height = 3 cm

Put base and height in formula:

$\longrightarrow \sf 6 \times 3$

$\longrightarrow \sf \pink{\boxed{\sf 18} \star}$

Area of parallelogram is 18 cm².

If we see parallelogram taking base 4 cm. Then area will be same.

So,

$\longrightarrow$ 18 = 4 × h

$\longrightarrow$ 18/4 = h

$\longrightarrow$ h = 4.5

Therefore,

Height corresponding to shorter side is 4.5 cm.

Answer 2

Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(6,6)\thicklines\put (0,0){\line (1,2){1.3}}\put (0,0){\line (1,0){5}}\put (5,0){\line(1,2){1.3}}\put (1.25,2.6){\line (1,0){5}}\put (1.27,0){\line (0,1){2.58}}\put (-0.35,-0.4){\sf B}\put (5.15,-0.15){\sf C}\put(6.21,2.74){\sf D}\put (1,2.74){\sf A}\put (1.1,-0.4){\sf E} \put (2.5,-0.8){\bf 6cm}\put (1.5,1.6){\sf 3cm}\put (0,1.4){\sf 4cm}\put (1.3,0){\framebox(0.2,0.3)}\end {picture}$

Answer:

$\huge \bf \: Given$

• Adjacent sides of parallelogram= 6 cm and 4 cm
• Height corresponding to longer side =3 cm

$\huge \bf \: To \: find$

Area of parallelogram and the height corresponding to the shorter side

$\huge \bf \: Solution$

$\sf \underline {firstly \: lets \: understand \: the \: conept}$

Here, is a parallelogram whose sides are 6 cm and 4 cm. And when height corresponding is longer 3 cm.

$\huge \bf \: Lets \: solve$

As we know that, Opposite sides of a parallelogram are equal.

Therefore,

The sides will be 6cm, 6 cm, 4cm, 4cm

Therefore larger side will be 6 cm. Smaller side will be 4 cm.

Height corresponding to 6 cm is 3 cm.

$\huge \fbox {Area = B × H}$

$\sf \mapsto \: area \: = 6 \times 3$

$\sf \mapsto area \: = {18 \: cm}^{2}$

Here, When we take base 4 cm. Then area will be same.

Therefore

$\sf \: area \: = base \times \: height$

$\sf \: 18 = 4 \times h$

$\sf \: h \: = \dfrac{18}{4}$

Height of smaller side = 4.5 cm.