Here we will discuss about the perimeter and area of a parallelogram and some of its geometrical properties.

Perimeter of a parallelogram (P) = 2 (sum of the adjacent sides)

= 2 × a + b

Area of a parallelogram (A) = base × height

= b × h

Some Geometrical Properties of a Parallelogram:

In the parallelogram PQRS,

PQ ∥ SR, PS ∥ QR

PQ = SR, PS = QR

OP = OR, OS = OQ

Area of the ∆PSR = area of the ∆QSR = area of the ∆PSQ = area of the ∆PQR = \(\frac{1}{2}\) (area of the parallelogram PQRS.

Area of the ∆POQ = area of the ∆QOR = area of the ∆ROS = area of the ∆POS = \(\frac{1}{4}\) (area of the parallelogram PQRS.

Solved Example Problem on Perimeter and Area of Parallelogram:

**1.** Two sides of a parallelogram are 12 cm and 9 cm. If the
distance between its shorter sides be 8 cm, find the area of the parallelogram.
Also find the distance between the longer sides.

**Solution:**

Area of the parallelogram PQRS = base × height

= PS × RM

= RS × PN.

Therefore, area of the parallelogram = 9 × 8 cm\(^{2}\) = 12 cm × PN

Therefore, 72 cm\(^{2}\) = 12 cm × PN

or, PN = \(\frac{72}{12}\) cm = 6 cm

Hence, the distance (PN) between the longer sides = 6 cm.

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