**Parallelogram Definition**

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

**Area of parallelogram**

Area = base \(\times\) height

= a\(\times\)b\(\times\)sinA = b\(\times\)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 ∠ABC = ∠CDA, ∠BCD = ∠DAB
- Sum of angles is equal to 360, i.e. ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°
- The sum of the angles adjacent to any sides is 180.

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

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 – b² = 5² + 11² – 2(11)(5)cos(115°) b² = 25 + 121 – 110(-.422) b² = 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 θ, so we use sine law 5/sin(θ) = 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 θ = h/22 h = 7.184 cm Area = base \(\times\) height A = 13.87 \(\times\) 7.184 A = 99.645 \(cm ^{2}\) |

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