Area of Parallelogram

Parallelogram is a plane shape that has two pairs of parallel sides and equal in length. Parallelogram has two pairs of angles that are not right-angled. Opposite corners of a parallelogram having the same large angle. Parallelogram with four equal sides is called a rhombus.

The properties of a parallelogram is as follows:

• Opposite sides are parallel and equal in length
• Opposite angles are equal  
• Adjacent angles  add up to 180°, so they are supplementary angles (Two Angles are Supplementary if they add up to 180 degrees).
• Both diagonals bisect each line segment equal in length.

AC and BD are diagonal of ABCD parallelogram.

• AB equal length and parallel to the CD.
• BC equal length and parallel to AD.
• ∠ BAD = ∠ BCD, ∠ CBA = ∠ ADC
• OA = OB = OC and OD

Area of parallelogram can be found using triangle area by divide through BD or AC diagonals, so there are 2 congruent triangle. ΔBAD and ΔBCD.
Area of parallelogram = 2 x Area of triangle
                                       = 2 x ½ (b x h)
                                       = b x h
The Area is the base x height :
Area = b × h
Than from the area  of parallelogram can be found the base and heigh.
b  = A/h and h = A/b


Example :
1.  Height of a parallelogram is 15 cm and base = 25. What is the area ?
     Area = b x h
              = 15 x 25
              = 375 cm
2.  Area of parallelogram is 595 cm, height 17 cm. What is the base ?
     Base = Area/height
              = 595/17
              = 35 cm
3.  Base of the parallelogram is 16 cm and volume = 192 cm. What is the height ?
      Height = Area/Base
                   = 192/16
                   = 12 cm