## Parallelogram Definition

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length & opposite angles are equal in measures.

## Area of parallelogram-

Area = baseÂ \(\times\) height

A = a\(\times\)b\(\times\)Â sinA = bÂ \( \times \)a\(\times\)sinB

## Properties of parallelogram

- Opposite sides have same length AB = CD, AD = BC.
- Opposite sides are parallel AB||CD & AD||BC
- Opposite angles are equal âˆ ABC = âˆ CDA & âˆ BCD = âˆ DAB
- Sum of angles is equal to 360, i.e. âˆ ABC + âˆ BCD + âˆ CDA + âˆ DAB = 360Â°
- The sum of the angles adjacent to any sides is 180.

âˆ ABC + âˆ BCD = âˆ BCD + âˆ CDA = âˆ CDA + âˆ DAB = âˆ DAB + âˆ DAB = 180Â° - Each diagonal divides the parallelogram into two equal triangles.
- Bisectors of adjacent parallelogram angle always intersect at right angles (90Â°)

Example- Find the area of a parallelogram whose base is 5 cm and height is 8 cm.
We know, Area = Base x Height Area = \(5 \times 8 \;cm^{2}\) Area = \( 40 \;cm^{2}\)
The angle opposite to the side b comes out to be 180 – 65 = 115\(^{\circ}\) We use the law of cosines to calculate the base of the parallelogram – bÂ² =Â 5Â² + 11Â² – 2(11)(5)cos(115Â°) bÂ² =Â 25 + 121 – 110(-.422) bÂ² = 192.48 b = 13.87 cm. After finding the base we need to calculate the height of the given parallelogram. To find the height we have to calculate the value of Î¸, so we use sine law 5/sin(Î¸) = b/sin(115) Now we extend the base and draw in the height of the figure and denote it as ‘h’. The right-angled triangle (marked with red line) has the Hypotenuse to be 22 cm and Perpendicular to be h. So sin Î¸ = h/22 h = 7.184 cm Area = baseÂ \(\times\) height A = 13.87 \(\times\) 7.184 A = 99.645 \(cm ^{2}\) |

Hope this discussion has made all your doubts clear regarding this Parallelogram and their properties. Visit BYJU’S to learn more about quadrilateralsÂ and many more.