Question

PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find the area of the parallelogram PQRS.


                                                   

Answer 1

Hint: We will solve this question by noting down all the given information in the question. By using the given figure and the formula of Area of the Parallelogram, i.e., Base \[ \times \] Height, and by putting the values in formula. We will get the result.

Complete step-by-step answer:
Given, PQRS is a Parallelogram, in which QM is the height from Q to SR and QN is the height from Q to PS.
We have SR = 12 cm and QM = 7.6cm.
Now, we have to find the area of parallelogram PQRS.
As the area of the parallelogram can be calculated by the formula i.e.
Area Of The Parallelogram = Base \[ \times \] Height
As shown in the figure,
Base = SR,
Height = QM
Therefore, the formula becomes,
Area of the Parallelogram = SR \[ \times \] QM
Now, by substituting the values of SR and QM from the question, we obtain

Area of the Parallelogram = 12 \[ \times \] 7.6
                                               = 12 \[ \times \] \[\dfrac{{76}}{{10}}\]
By multiplication, we get
                                               = \[\dfrac{{912}}{{10}}\]
                                               = \[91.2c{m^2}\]

Hence, the area of the Parallelogram is \[91.2c{m^2}\].

Note – A Parallelogram is a four-sided rectilinear figure whose opposite or facing sides are of equal length and the opposite angles are of equal measure. While solving these kinds of questions, one should be clear and sure about the formula, otherwise there are chances of mixing up the different formulas. Hence, we don’t know the value of QN and PS so this is the only way to obtain the answer.