What are Rhomboids?
In geometry, a rhomboid is a two-dimensional shape in which the adjacent sides have unequal lengths, and all the angles do not necessarily measure 90 degrees, that is, these angles are non-right angles. A rhomboid is said to be a type of parallelogram as the opposite sides are parallel, and the opposite angles are equal. If all the angles in a rhomboid are equal, then, it will become a rhombus. Although all rhombuses are rhomboids, not all rhomboids are always rhombuses.
What are the Properties of a Rhomboid?
The following is a list of the properties of a rhomboid:
- The opposite sides of a rhomboid are parallel and equal
- A rhomboid is divided along the diagonal into two congruent triangles
- A rhomboid has equal and opposite angles
- The internal angles of a rhomboid add up to a 360° angle.
- The image gives us a better understanding of these properties:
- Sides AD and AB are parallel to sides BC and CD, respectively
- Side AB = CD, while side AD = BC
- The opposite angles are, ∠ADC = ∠ABC and ∠DAB = ∠DCB
- The sum of the angles, ∠A + ∠B + ∠C + ∠D = 360°
Basic Formulas for Rhomboids
Now that we know the properties of a rhomboid, we are going to learn the two most often used formulas for a rhomboid, area and perimeter.
Area of a Rhomboid:
The amount of space taken by a rhomboid is called the area of the rhomboid. It can be determined with the equation,
Area of Rhomboid = Base × Height.
Perimeter of a Rhomboid:
The total length of the boundary of a rhomboid is its perimeter. The perimeter can be calculated by the following formula,
Perimeter of Rhomboid = 2(a + b)
Where ‘a’ is the length of one side and ‘b’ is the length of the other side of the rhomboid.
Rapid Recall
Solved Rhomboid Examples
Example 1:
Ross wants to make a kite for his friend. So he bought a bunch of color sheets and started cutting them. While cutting the papers, Ross is stuck as he doesn’t know how much paper to cut to make a 12 x 15 cm sized kite. Help Ross to find the required amount of paper.
Solution:
Ross wants to make a kite of length 12 x 15 cm.
As we know, the shape of a kite is a rhomboid. Then, we can consider b = 12 and h = 15
In order to find the required amount of paper to make a kite, let’s find the area of the kite.
And the formula to find the area of a rhomboid Area = Base x Height
= 12 x 15 [Multiply]
= 180 square cm
Therefore, Ross requires 180 square centimeters of paper to make a kite for his friend.
Example 2:
If a rhomboid has a perimeter of 50 cm, and the length of one side is 10 cm, find the length of the other side of the rhomboid.
Solution:
Let WXZY be a rhomboid.
As mentioned, Perimeter, P = 50 cm
Let one side be WX, that is WX = 10 cm
As we know, the opposite sides of a rhomboid are congruent to each other.
Thus, WX = YZ = 10 cm
To find WY and ZX, let’s use the formula
P = 2WX + 2XZ
50 = 2(10) + 2XZ [Put values]
50 = 20 + 2XZ
50 – 20 = 2XZ [Subtract]
30 = 2XZ
\(\frac{30}{2}\) = XZ [Divide both sides by 2]
XZ = 15
Hence, the other side of the rhomboid is 15 cm.
Therefore, the measurements of the sides of the rhomboid WXZY are: 10 cm and 15 cm.
Example 3:
Emily has bought a small piece of crystal in a diamond shape to decorate her table that has a shape of height 3 cm. If the area of this crystal is 15 cm, what would be the length of its base?
Solution:
As mentioned, the area of the crystal is 15 cm and the height of the crystal is 3 cm.
Since the shape of the crystal is a rhomboid, we can use the formula to find the area of a rhomboid.
Then,
Area of Rhomboid = Base × Height.
15 = Base × 3
5 = Base.
Hence, the base of Emily’s crystal is 5 cm in length.
The main difference between a rhomboid and a rhombus is that all the sides in a rhombus have equal lengths. Thus, all rhombuses are rhomboids, but not all rhomboids are rhombuses.
Yes, the internal angles of a rhomboid add up to 360° according to the angle sum property of quadrilaterals.
Rhomboids can have many different shapes, but they always resemble a lopsided diamond or a rectangle.
Yes, a rhomboid is a parallelogram with no right angles and the adjacent sides are of different lengths.