Question

PQRS is a Parallelogram . QM is the Height from Q to SR and QN is the height from Q to PS. If SR = 12cm and QM = 7.6cm . Find :

(a) The area of Parallelogram PQRS
(b) QN , If PS = 8cm.



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Answer 1

Step-by-step explanation:

Given: SR=12cm, QM=7.6cm, PS=8cm.

Area of parallelogram=base×height

=12×7.6=91.2cm

Area of parallelogram=base×height

⇒91.2=8×QN

⇒QN= 91.2/8

=11.4cm.

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Answer 2

Given -

• QM is the Height from Q to SR and QN is the height from Q to PS.

• SR = 12 cm and QM = 7.6 cm

To find -

• Area of parallelogram

• QN, if PS is 8cm

Formula used -

• Area of parallelogram.

Solution -

In the question, we are provided with 2 heights from some points (like Q), And we need to find the area of parallelogram and QN. For that first we will take SR as the base and QM as the height, then we will multiply them both, that will give us the area of parallelogram PQRS. After that, we will find QN, if PS is 8cm, by dividing the obtained area with the 8, that will give us the value of QN. Let's do it!

So -

Let SR be the base with length 12cm and QM as the height with 7.6 cm

$\sf \underline{area \: of \: parallelogram} \: = base \: \times \: height$

On substituting the values -

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

$\sf \longrightarrow \: area \: = 12 \: cm \: \times \: 7.6 \: cm$

$\sf \longrightarrow \: area \: = 91.2 \: {cm}^{2}$

Now -

Now, we will find the value of QN, By dividing the obtained area with 8, by again applying the formula of area of parallelogram.

Let -

PS be the base with length 8cm and, QN be the height, with height x

$\sf \underline{area \: of \: parallelogram} \: = base \: \times \: height$

On substituting the values -

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

$\sf \longrightarrow\: 91.2 \: = 8 \: \times x$

$\sf \longrightarrow \: x \: = \dfrac{91.2}{8}$

$\sf \longrightarrow \: x \: = 11.4 \: cm$

$\therefore$ The area of parallelogram PQRS is 91.2cm² and value of QN is 11.4cm

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