# Area of Parallelogram

## What is a parallelogram?

A parallelogram is a 2-dimensional (meaning flat) figure or shape, bounded by four sides and both pairs of opposite sides parallel.  This article is on area of a parallelogram. Some of the properties of a parallelogram are:

• Opposite sides are parallel.
• Opposite sides are equal.
• Opposite interior angles are equal.
• Diagonals bisect each other.
• Diagonals bisect the interior angles.

A parallelogram fits the definition of a quadrilateral. There can be some special types of parallelograms like rectangle, rhombus and square.

## Area of a Parallelogram

Area is basically the quantity that expresses the measure of the extent of a 2-dimensional figure or shape. We can recall that if we have a rectangle with base “b” and height “h”, then the area of the rectangle is base times height.

Area of Rectangle = base x height = b x h

We will now show with the help of the following figure that every parallelogram can be converted to a rectangle. If we take any vertex of a parallelogram and drop a perpendicular from it to the opposite side, then what we get is shown in the figure. This blue colored triangle can just be rearranged to form rectangle as shown. The area covered by the two figures has to be same in principle. Thus the area of the parallelogram can be given by area of the newly obtained rectangle. Hence,

Area of Parallelogram = base x height = b x h

## Solved Examples

Question 1: Find the area of a parallelogram shown in figure.

Solution:

Formula for the area of a parallelogram is  base x height.

Hence, Area of parallelogram =2.5 m x 1.8 m  = 4.5 m2

Question 2: Find the height of a parallelogram of base 6 cm and area 24 cm2.

Solution:

Base of the parallelogram = b = 6 cm.

Area of the parallelogram = A = 24 cm2.

Height of the parallelogram = h = ?

Area of the parallelogram  = A =  b x h
⇒ 24 cm2 =  6 cm x h cm

⇒ h = (24/6) cm

⇒ h = 4 cm
Question 3: The area of parallelogram PQRS is 88 cm2. A perpendicular from P is drawn to intersect QR at T. If PT= 8 cm and TR= 5 cm, then find the length of PQ.
Solution:
Area of parallelogram PQRS = A = 88 cm2
PT = h = 8 cm
We know that area A = base x height
⇒ A = b x h
⇒ 88 cm=  8 cm x b cm
⇒ b = 11 cm.
QR = b = 11 cm
TR = 5 cm
QT = QR – TR = (11 – 5) cm = 6 cm.
By Pythagoras Theorem,
QT2 + PT2  = PQ2
⇒ 62 +  82  =  PQ2
⇒ PQ = 10 cm