Class 7    Math    Area of Geometrical Shapes
Calculate Area of a Parallelogram

Question: Find area of the below parallelogram, when its length is 11 cm and height is 5 cm.

     

Answer: This is a simple problem based on calculating area of a shape. We are aware of calculating areas of different shapes like rectangle, square, circle, triangle, etc. In this question the shape is parallelogram. Its length is DC, which is given as 11cm and height AE is given as 5 cm.

As we know that area of a parallelogram is length × breadth (l x b). Length in this diagram is DC or AB and breadth in this diagram is AD or BC. As per the question we have only length and length of a perpendicular line from one of its corner to its base. In order to calculate the area of this parallelogram, let us redraw this diagram as shown below:

     

Here, we have drawn a parallel line to AE, which is BF and extended the length of the parallelogram till CF. If we look closely, the length of DE and CF are equal. We have drawn a perpendicular line on DC from the point B.

Look at the points ABFE, it has shape of a rectangle and we know that the area of a rectangle is multiplication of its length and width. Let us see below diagram for a better understanding:

     

It is much easier to calculate area of this diagram (which is a rectangle). The area will be:
  = 11 cm x 5 cm
  = 55 cm (2)

So the area of the parallelogram is 55 cm2

From this question we also understand that, area of a parallelogram:
  = base x height
  = b x h