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.

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

= b ⋅ 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

= b ⋅ 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

= b ⋅ 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

b ⋅ h = 14/3

b ⋅ 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

b ⋅ h = 40

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

b ⋅ 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

= b ⋅ 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

b ⋅ h = 60

Substitute b = 12 and h = x.

12 ⋅ x = 60

Divide each side by 12.

x = 5

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