## Parallelogram Definition

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and the opposite angles are equal in measure.

## Area of Parallelogram –

Below is the formula to find the parallelogram area:

Area = Base Ã— Height

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

## Properties of Parallelogram

If a quadrilateral has a pair of parallel opposite sides, then itâ€™s a special polygon called Parallelogram. A parallelogram has six important properties.

The opposite sides of a parallelogram are congruent. |

The opposite angles of a parallelogram are congruent. |

The consecutive angles in a parallelogram are supplementary. |

If any one of the angles of a parallelogram is right, then all the other angles will be right. |

The two diagonals in the parallelogram bisect each other. |

The diagonals of the parallelogram separate it into congruent. |

## Types of Parallelogram

There are mainly four types of Parallelogram depending on various factors. The factors which distinguish between all of these different types of parallelogram are angles, sides etc.

- In a parallelogram, say PQRSÂ
- If PQ = QR = RS = SP are the equal sides, then itâ€™s a rhombus. All the properties are the same for rhombus as for parallelogram.

- Other two special types of parallelogram are:

- Rectangle
- Square

**Read More **on Types of Parallelogram

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 \(cm ^{2}\) |

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