AREA OF PARALLELOGRAM

A parallelogram is a quadrilateral in which opposite sides are parallel and equal in length.

In other words opposite sides of a quadrilateral are equal in length, then the quadrilateral is called a parallelogram.

The area of a parallelogram is the product of a base and  its corresponding height.

Then, the formula to find area of a parallelogram is given by

A  =  b ⋅ h square units

We can justify the area for parallelogram as follows. 

The area of a parallelogram is the area of a rectangle with the same base and height. 

Examples

Example 1 : 

Find the area of the parallelogram ABCD shown below. 

Solution :

Method 1 : 

Use AB as the base.

So, b  =  16 and h  =  9.

Formula for area of a parallelogram is 

=  ⋅ h

Substitute the given measures. 

=  16 ⋅ 9

=  144 square units

Method 2 : 

Use AD as the base.

So, b  =  12 and h  =  12.

Formula for area of a parallelogram is 

=  ⋅ h

Substitute the given measures. 

=  12 ⋅ 12

=  144 square units

Example 2 : 

Find the area of the parallelogram ABCD shown below. 

Formula for area of a parallelogram is 

=  ⋅ h

Substitute b  =  5 and h  =  3.

=  5 ⋅ 3

=  15 square units

Example 3 :

A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 square yards. The height of each parallelogram is 1 1/3 yards. How long is the base of each parallelogram ?

Solution :

Because the given parallelograms are congruent area of two parallelogram will be equal. 

Combined area of parallelograms  =  9 1/3 square yards

Combined area of parallelograms  =  28/3 square yards

Area of one parallelogram  =  (28/3) ÷ 2

Area of one parallelogram  =  14/3

⋅ h  =  14/3

⋅ 1 1/3  =  14/3

b ⋅ 4/3  =  14/3

Multiply each side by 3/4.

b  =  14/3 ⋅ 3/4

b  =  14/4

b  =  7/2

b  =  3 1/2

So, the base of the parallelogram is 3 1/2 yards.

Example 4 :

Find the base of a parallelogram if its area is 40 square cm and its altitude is 15 cm.

Solution :

Area of a parallelogram  =  40 cm2

 h  =  40

Here, altitude (or) height (h)  =  15 cm.

 15  =  40

Divide each side by 15.

b  =  2.67

So, the base of the parallelogram is 2.67 inches. 

Example 5 : 

Find the area of the shape shown below. 

The above shape has four sides. So, it is a quadrilateral. Because the opposite sides are parallel, the above quadrilateral is a parallelogram. 

Formula for area of a parallelogram is 

=  ⋅ h

Substitute b  =  9 and h  =  4.

=  9 ⋅ 4

=  36 square units

Example 6 :

If the area of the shape shown below is 60 square inches, then find the value of x. 

Solution :

Given : Area of the above shape is 60 square inches.  

The above shape has four sides. So, it is a quadrilateral. Because the opposite sides are parallel, the above quadrilateral is a parallelogram. 

Area  =  60 in2

 h  =  60  

Substitute b  =  12 and h  =  x.

12  x  =  60

Divide each side by 12.

x  =  5

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