Area of a Parallelogram Calculator | Free Online Area of a Parallelogram Calculator with Steps - BYJUS

# Area of a Parallelogram Calculator

The area of a parallelogram calculator is a free online tool that helps us calculate the area of a parallelogram, as well as its base length and height. Let us familiarize ourselves with the calculator....Read MoreRead Less

## Online Area of a Parallelogram Calculator

### How to Use the ‘Area of a Parallelogram Calculator’?

Follow these steps to use the ‘Area of a parallelogram calculator’:

Step 1: Enter the two known measures (out of base length, height and area) into the respective input boxes and the unknown measure will be calculated.

Step 2: Select the appropriate units for the inputs and output.

Step 3: Click on the ‘Solve’ button to obtain the result.

Step 4: Click on the ‘Show steps’ button to know the stepwise solution to find the missing measure.

Step 5: Click on the   button to enter new inputs and start again.

Step 6: Click on the ‘Example’ button to play with different random input values.

Step 7: When you click on the ‘Explore’ button, you can visualize the parallelogram by changing its dimensions and also how the area of a parallelogram relates to the area of a rectangle.

Step 8:  When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.

### What is the Area of a Parallelogram?

The amount of region occupied within the four sides of a parallelogram is known as the area of a parallelogram. The area of a parallelogram is equal to the product of its base length and height.

### Formulas used in the ‘Area of parallelogram calculator’:

When the base length b and height h of the parallelogram are known, the area of a parallelogram A is calculated as:

Area of parallelogram, A = b $$\times$$ h

When the base length b and the area of a parallelogram A are known, the height h of the parallelogram is calculated as:

Height of parallelogram, $$h=\frac{A}{b}$$

When the height h and the area of a parallelogram A are known, the base length b of the parallelogram is calculated as:

Base length of parallelogram, $$b=\frac{A}{h}$$

### Relation between the area of a parallelogram and the area of a rectangle

Consider a rectangle of base length b and height h,

The area of the rectangle, A = b $$\times$$ h

Now consider a parallelogram of base length b and height h. As we can see in the figure below, the parallelogram can be split into two right triangles of base length x and height h and a rectangle of base length y and height h.

Therefore, the area of this parallelogram can be written as:

Area of parallelogram = Area of two right triangles + Area of the rectangle

= $$2 \times \frac{1}{2}\times x \times h+y \times h$$

= (x + y) h

= $$b \times h$$

Hence, we can say that a rectangle and parallelogram having the same base length and height will have the same area.

### Solved Examples on Area of a Parallelogram Calculator

Example 1: Find the area of a parallelogram having a base length of 5 inches and a height of 6 inches.

Solution:

Area of parallelogram, A = b $$\times$$ h

= 5 $$\times$$ 6

= 30 square inches

So, the area of the parallelogram is 30 square inches.

Example 2: Find the height of a parallelogram whose base length is 50 meters and area is 257 square meters.

Solution:

Height of parallelogram, h = $$\frac{A}{b}$$

= $$\frac{257}{50}$$

= 5.14 meters

So, the height of the parallelogram is 5.14 meters.

Example 3: Find the base length of a parallelogram having a height of 7 centimeters and an area of 76 square centimeters.

Solution:

Base length of parallelogram, b = $$\frac{A}{h}$$

= $$\frac{76}{7}$$

= 10.857 centimeters

So, the base length of the parallelogram is 10.857 centimeters.

Frequently Asked Questions on Area of Parallelogram Calculator

A quadrilateral that has opposite sides of equal lengths and are parallel to each other, and whose diagonals bisect each other is known as a parallelogram

Yes, a square is a parallelogram because it fulfills the conditions of a parallelogram, that is, a square has opposite sides which are equal in length and are also parallel to each other, and its diagonals bisect each other

The perimeter of a parallelogram is the sum of the lengths of all its sides.

Therefore, the formula for finding the perimeter of a parallelogram is:

Perimeter, P = 2(a + b) units where, ‘a’ and ‘b’ are the lengths of the adjacent sides of the parallelogram.