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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