A rhomboid is a two-dimensional shape which is similar to a parallelogram but different from a rhombus. It can be said that all rhombuses are rhomboids, but all rhomboids may not be rhombuses.
|1.||What is a Rhomboid?|
|2.||Properties of a Rhomboid|
|3.||Formulas of a Rhomboid|
|4.||Solved Examples on Rhomboid|
|5.||Practice Questions on Rhomboid|
|6.||FAQs on Rhomboid|
What is a Rhomboid?
A rhomboid is a quadrilateral in which the opposite sides are parallel and the opposite angles are equal. It is similar to a parallelogram because its opposite sides are parallel and it can become a rhombus if all its sides are equal. Observe the following rhomboid with altitude (height) 'h' and base 'b' and side 'a'.
Properties of a Rhomboid
Here is a list of the properties of a rhomboid:
- In a rhomboid, the opposite sides are parallel and equal.
- The diagonal divides the rhomboid into two congruent triangles.
- The opposite angles of a rhomboid are congruent.
- The sum of interior angles of a rhomboid is equal to 360°.
Now, let us relate these properties to the following figure.
- Side AD is parallel to BC and AB is parallel to CD. Side AD = BC and AB = CD.
- Diagonal AC divides the rhomboid into two congruent triangles ABC and ADC. Diagonal BD divides the rhomboid into two congruent triangles ABD and BCD
- The opposite angles are: ∠ADC = ∠ABC and ∠DAB = ∠DCB
- The sum of the angles: ∠A + ∠B + ∠C + ∠D = 360°
Formulas of a Rhomboid
Let us learn about the two basic formulas of a rhomboid.
Perimeter of a Rhomboid
The perimeter of a rhomboid is the total measurement of its boundary. The formula for the perimeter of a rhomboid is the sum of all its sides. We know that the opposite sides of a rhomboid are equal. This means side AD = BC and AB = CD. In the following figure, BC is marked as 'a' and AB is marked as base (b). This makes the perimeter formula: 2(a+b).
Perimeter of Rhomboid = a + a + b + b = 2(a + b), where 'a' is the length of one side of the rhomboid and 'b' is the base of the rhomboid.
Area of a Rhomboid
The amount of space occupied by a rhomboid is called the area of a rhomboid. Since the diagonal of a rhomboid divides it into two congruent triangles, the area of a rhomboid becomes twice the area of a triangle, i.e., 2 × [ ½ × base × height]. So, the formula for the area of a rhomboid is:
Area of Rhomboid = 2 × [ ½ × base × height] = base × height. The area of a rhomboid is represented in square units. Observe the following rhomboid with altitude (height) 'h' and base 'b' and side 'a'.
Related Articles on Rhomboid
Check out the links of interesting articles related to a rhomboid.
Solved Examples on Rhomboid
Example 1. Calculate the area of a rhomboid with a base of 8 inches and the altitude (height) as 5 inches.
Base of the rhomboid = 8 inches; height of the rhomboid = 5 inches
Area of Rhomboid = base × height = 8 × 5 = 40 in²
Therefore, the area of the rhomboid is 40 in².
Example 2. Find the height of a rhomboid whose area is 50 square units and the base is 10 units. What is its perimeter if the adjacent side is 7 units?
Base of the rhomboid = 10 units; area of the rhomboid = 50 square units.
Area of a Rhomboid = base × height
Area = 10 × h
50 = 10 × h
h = 5.Therefore, the height of the rhomboid is 5 units.
Perimeter of a rhomboid = 2 (a + b); where a = 7 units, b = 10 units
Substituting the values in the formula: 2 (10 + 7) = 34
Therefore, the perimeter of the rhomboid is 34 units.
FAQs on Rhomboid
What is the Shape of a Rhomboid?
A rhomboid is a flat, two-dimensional shape which is similar to a parallelogram and slightly different from a rhombus. According to the two-dimensional geometry, it is a parallelogram in which the adjacent sides are not equal and the angles are not right-angled. If all the sides of a rhomboid become equal it becomes a rhombus.
Does a Rhomboid Add up to 360?
Yes, according to the angle sum property of a quadrilateral, the sum of the interior angles of a rhomboid is equal to 360°.
Is Every Square a Rhombus?
Yes, every square is a rhombus because a square fulfills the main properties of a rhombus. The opposite sides of a square are parallel and congruent to each other which brings it under the category of a rhombus.
Does a Kite Add up to 360?
A kite is a quadrilateral, and according to the angle sum property of a quadrilateral the sum of all interior angles of any quadrilateral is equal to 360°.
Is a Rhomboid a Rhombus?
No, a rhomboid may not necessarily be a rhombus. A rhomboid is a two-dimensional shape which is similar to a parallelogram but different from a rhombus. If all the sides of a rhomboid become equal it becomes a rhombus. It can be said that all rhombuses can be rhomboids, but all rhomboids may not be rhombuses.