Rhomboid

Rhomboid is a close geometric figure in which opposite sides are parallel to each other. Rhomboid is different from Rhombus. Rhomboid is a type of parallelogram. Since, in a Rhomboid opposite sides are parallel it is a parallelogram, however, all sides are not equal, hence it is not a rhombus.

In this article, we are going to discuss what a is Rhomboid in Geometry, the properties of a rhomboid, the difference between a Rhombus and a Rhomboid, formula for calculating the area and perimeter of a Rhomboid.

What is a Rhomboid?

A Rhomboid is a two-dimensional figure in geometry. It is a quadrilateral in which opposite sides are equal and parallel. A rhomboid is similar to a parallelogram. Adjacent sides of the rhomboid are not equal and only opposite sides are equal, hence it is termed a Parallelogram. Rhomboid is different from Rhombus. In case, if all sides of rhomboid become equal then it will become a rhombus. If we draw a diagonal in the Rhomboid then it divides the Rhomboid in two congruent triangles.

Definition of Rhomboid

A rhomboid is a type of parallelogram in which opposite sides are equal and parallel. The interior angle of the Rhomboid is not equal to 90 degree. A Rhomboid is a two-dimensional figure, which is a shape in geometry and totally different from Rhombus.

Properties of Rhomboid Shape

Some properties of rhomboid are mentioned below:

• Adjacent Sides of Rhomboid are not equal.
• The interior angle of Rhomboid , which are bounded by adjacent sides are not equal to 90 deg.
• Rhomboid is a type of parallelogram.
• A rhombus is always a rhomboid , but a rhomboid is not always a rhombus.
• Opposite sides of rhomboid are parallel.
• Opposite sides of rhomboid are equal.
• Opposite angles of Rhomboid are equal.
• As, in the case of all quadrilateral , sum of all interior angle of rhomboid is 360 deg.
• The opposite angles of a rhomboid are congruent.
• The diagonal of rhomboid divides it into two congruent triangles.

Rhombus vs Rhomboid

Rhombus and Rhomboid sounds similar but are two different geometric figures. The difference between Rhombus and Rhomboid are mentioned below:

Difference between Rhombus and Rhomboid
Rhombus	Rhomboid
All four sides of rhombus are equal.	All four sides of rhomboid are not equal. Opposite sides of rhomboid are parallel and equal.
The interior angle of rhombus is not equal to 90 degree.	The interior angle of rhomboid are not equal to 90 deg.
A rhombus is a rhomboid.	A rhomboid is not a rhombus.

Perimeter of Rhomboid

Rhomboid is a type of parallelogram in which opposite sides are equal unlike in rhombus in which all four sides are equal. We can find formula for calculating perimeter of Rhomboid similar as we calculate the perimeter of rectangle. If opposite sides are equal then if we suppose the lengths of adjacent sides of rhomboid are a and b, then perimeter of rhomboid = a + b + a + b = 2a + 2b = 2 (a + b).

Perimeter of Rhomboid = 2 (a + b)

Area of Rhomboid

Area of Rhomboid is calculated by finding the area of two congruent triangle present inside rhomboid. If we calculate the area of one triangle then we get the total area of rhomboid by just multiplying 2 into it. The area of triangle is calculated by using the formula 1/2 ⨉ base ⨉ height.

So, the area of rhomboid is equal to 2 ⨉ 1/2 ⨉ base ⨉ height = base ⨉ height.

Area of Rhomboid = base ⨉ height

Volume of Rhomboid

Volume of rhomboid cannot be calculated because it is a plane two-dimensional figure. Volume is only calculated for three-dimensional objects.

Rhomboid Formula

Since, Rhomboid is a two dimensional figure, hence its perimeter and area can be calculated only. The formula for the same is discussed below:

Perimeter Formula of Rhomboid

For a Rhomboid with sides “a” and “b”, its perimeter can be calculated as

Perimeter of Rhomboid Formula = 2 (a + b)

Area Formula of Rhomboid

For a Rhomboid with base and height, the area of Rhomboid can be calculated as

Area of Rhomboid = base ⨉ height

Practice Problems on Rhomboid

Eaxmple 1: What is perimeter of rhomboid having adjacent sides of length 7cm and 9cm?

Solution:

Perimeter of rhomboid = 2 (a + b)

a = 7cm , b = 9cm

= 2 (7 + 9) = 2 (16) = 32 cm.

The perimeter of rhomboid is 32 cm.

Example 2: What is area of rhomboid having base equal to 7cm and height is equal to 5cm?

Solution:

Area of Rhomboid = base ⨉ height

base = 7cm and height = 5cm

Area of Rhomboid = 7 ⨉ 5 = 35 cm2.

The Area of rhomboid is 35 cm² .

Example 3: If the perimeter of rhomboid is 50 cm and length of one side is 16cm then find the length of another adjacent side and also calculate the area of rhomboid.

Solution:

Perimeter of Rhomboid = 2(a + b)

a = 16cm , b = ?

perimeter = 2(16 + b) = 50

⇒ (16 + b) = 25

⇒ b = 25 – 16 = 9 cm.

⇒ a = 16 cm and b = 9cm

Another Adjacent side of Rhombus is 9 cm.

Now, Area of rhomboid = base ⨉ height

16 ⨉ 9 = 144 cm² .

Area of Rhomboid is 144 cm².

Practice Questions on Rhomboid

Q1. Find the area of rhomboid having base equal to 10 cm and height equal to 6 cm.

Q2. What is the perimeter of Rhomboid having length of its adjacent sides equal to 15cm and 10cm ?

Q3. If the perimeter of rhomboid is 70 cm and length of one side is 15 cm then, find the length of another adjacent side and also calculate the area of rhomboid.

Q4. If the area of Rhomboid is 90 cm², and height of rhomboid is 9 cm, then find the length of base of Rhomboid.

FAQs on Rhomboid

1. Is Rhombus and Rhomboid are similar shapes?

No, Rhombus and Rhomboid are two different figures. In Rhombus all sides are equal but in Rhomboid opposite sides are equal and parallel. Rhomboid is a type of parallelogram.

2. Can Volume for Rhomboid is calculated?

We cannot calculate volume of a rhomboid because it is two-dimensional figure. Volume is calculated for three dimensional figure.

3. What is Formula for Calculating Area and Perimeter of Rhomboid?

The Area and Perimeter Formula of Rhomboid is mentioned below:

• Formula for calculating Area of Rhomboid = base ⨉ height
• Formula for calculating perimeter of Rhomboid = 2 (a + b)

4. Is a Rhomboid a Rhombus?

No, a rhomboid may not necessarily be a rhombus.

5. Is a Rhombus a Rhomboid?

Yes, Rhombus is always a Rhomboid as Rhombus satisfies the property of a Rhomboid

6. What is Sum of Angles in a Rhomboid?

Yes, like other quadrilateral the sum of all four angles in rhomboid is equal to 360 degree.

7. Why Rhomboid is called similar to Parallelogram?

Rhomboid is similar to parallelogram because opposite sides of rhomboid are also equal and parallel.

8. Is every Square a Rhombus?

Yes, every square is a Rhombus.

9. Are Rhomboid and Parallelogram same?

Yes, parallelogram and Rhomboid are geometrically same

10. How many Lines of Symmetry are there in Rhomboid?

There is no line of symmetry in Rhomboid