Question

PQRS is a parallelogram. QM is the
perpendicular from Q to SR and QN N
is the perpendicular from Q to PS.
If SR = 12 cm and QM = 6 cm, find
the area of a parallelogram PQRS.
Also find QN if PS = 4 cm.

plsss answerr​

Answer 1

SR=12cm, QM=6cm, PS=4cm.

Area of parallelogram=base×height

12×6=72 cm^2

Area of parallelogram=base×height

72=4×QN

QN=72/4=18 cm

Answer 2

${\large{\sf{\pmb{\underline{Understanding \; the \; question...}}}}}$

☀ According to the question, there is a parallelogram given and it named as ${\red{\sf{PQRS}}}$. Guys, I attach a figure as attachment here, kindly see it too to understand the question properly.

☀ As ${\red{\sf{PQRS}}}$ is a parallelogram.${\red{\sf{QM}}}$ is the height of this parallelogram. ${\red{\sf{SR}}}$ is base here. ${\red{\sf{QM}}}$ is the perpendicular from ${\red{\sf{Q}}}$ to ${\red{\sf{SR}}}$ and ${\red{\sf{QN}}}$ is the perpendicular from ${\red{\sf{Q}}}$ to ${\red{\sf{PS}}}$ If ${\red{\sf{SR}}}$ measure 12 cm and ${\red{\sf{QM}}}$ measure 6 cm, find the area of a parallelogram ${\red{\sf{PQRS}}}$. Also find ${\red{\sf{QN}}}$ if ${\red{\sf{PA}}}$ measure 4 cm.

☀ What to find out?

• We have to find out the area of this parallelogram.

• And we have to find the measurement of QN too if PS is given as 4 centimetres.

${\large{\sf{\pmb{\underline{Given \; that...}}}}}$

$\bigstar \sf QM \: is \: the \: height \\ \\ \bigstar \sf QM \: measures \: 6 \: cm \\ \\ \bigstar \sf SR \: measures \: 12 \: cm \\ \\ \bigstar \sf SR \:is \: the\: base \\ \\ \bigstar \sf PS \: measures \: 4 \: cm$

${\large{\sf{\pmb{\underline{To \; find...}}}}}$

$\bigstar \sf Area \: of \: parallelogram \\ \\ \bigstar \sf Measurement \: of \: QN$

${\large{\sf{\pmb{\underline{Solution...}}}}}$

$\bigstar \sf Area \: of \: parallelogram \: = 72 \: cm^{2} \\ \\ \bigstar \sf Measurement \: of \: QN \: 18 \: cm$

${\large{\sf{\pmb{\underline{Using \; concepts...}}}}}$

$\bigstar \sf Area \: of \: parallelogram \: formula \\ \\ \bigstar \sf Measurement \: of \: QN \: formulas \: (atq)$

${\large{\sf{\pmb{\underline{Using \; formulas...}}}}}$

${\small{\underline{\boxed{\frak{Area \: of \: parallelogram \: = Base \times Height}}}}}$

${\small{\underline{\boxed{\frak{QN \: = \dfrac{Area \: of \: parallelogram}{PS \: measurement}}}}}}$

${\large{\sf{\pmb{\underline{Here,}}}}}$

$\bigstar \sf Area \: is \: ? \\ \\ \bigstar \sf Height \: is \: 12 \: cm \\ \\ \bigstar \sf Base \: is \: 12 \: cm \\ \\ \bigstar \sf PS \: = 4 \: cm \\ \\ \bigstar \sf Area \: is \: (Have \: to \: find)$

${\large{\sf{\pmb{\underline{Full \; Solution...}}}}}$

~ Firstly let us find the area of the parallelogram..!

↝ Area = Base × Height

↝ Area = 12 × 6

↝ Area = 72 cm²

• Henceforth, 72 cm² is the area of the parallelogram.

~ Now let's find the measurement of QN..!

↝ QN = Area/PS

↝ QN = 72/4

↝ QN = 36/2

↝ QN = 18 cm

• Henceforth, 18 cm is the measurement of QN.