how to draw a rhombus 3d

Rhombus

A rhombus is a closed two-dimensional plane effigy. Information technology is considered a special parallelogram, and because of its unique backdrop, it gets an individual identity as a quadrilateral. A rhombus is as well chosen an equilateral quadrilateral since all of its sides are equal in length. The term 'rhombus' has been derived from the ancient Greek word 'rhombos', which actually ways something that spins. Allow us acquire more about the rhombus and its properties in this commodity.

1.	What is a Rhombus?
2.	Properties of a Rhombus
3.	What does a Rhombus look like?
iv.	Rhombus Formulas
5.	FAQs on Rhombus

What is a Rhombus?

A rhombus can exist defined as a special parallelogram as information technology fulfills the requirements of a parallelogram, i.east. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a foursquare. That is why it is besides known every bit a tilted square. Look at the prototype below to empathize the human relationship of rhomb shape with parallelogram and foursquare.

In the above figure, we tin notice that every rhomb nosotros see will besides be a parallelogram, but non every parallelogram is a rhombus. A square can exist considered as a special instance of a rhomb because information technology has four equal sides. All the angles of a square are right angles, just the angles of a rhombus demand not necessarily have to exist right angles. And, hence a rhombus with right angles can be considered a square. Hence, we tin conclude that:

• All rhombi or rhombuses are parallelograms, but all parallelograms are not rhombuses.
• All rhombi or rhombuses are not squares, simply all squares are rhombuses.

A rhombus can have 3 additional names:

• Diamond
• Lozenge
• Rhombus

Properties of a Rhombus

A rhombus is considered to be one of the special parallelograms as it has all the backdrop of a parallelogram. A rhombus has its two diagonals as its ii lines of symmetry. Axis of symmetry can be considered as a line that divides an object into 2 equal halves. It creates a mirror-like reflection of both sides of the object. A rhomb is said to have reflection symmetry over both of its diagonals. The general properties of a parallelogram are as follows:

• Reverse angles are congruent or equal.
• The contrary sides are equal and parallel.
• Diagonals bisect each other.
• The sum of any two adjacent or sequent angles is 180°.

A rhombus, like all geometric shapes, has properties that are unique to it. The table below describes the properties of a rhomb.

Backdrop of Rhomb	Reference
All sides of a rhombus are congruent (equal).	Here, AB = CD = DA = BC
Diagonals bisect each other at 90° or nosotros can too say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.	Hither, diagonals DB and CA bifurcate each other at xc°
Opposite angles are equal and the opposite sides are parallel.	Hither, CD || AB and BC || AD. ∠A = ∠C and ∠D = ∠B
Adjacent angles add together upwards to 180°	∠A + ∠B = 180° ∠B + ∠C = 180° ∠C + ∠D = 180° ∠A + ∠D = 180°

One affair we should recollect well-nigh the diagonal of a rhombus is that in addition to bisecting each other at xc°, the 2 diagonals bisected will be of the same length. For example: if the length of a diagonal is 10 cm and the other diagonal bisects it, then it is divided into two 5 cm segments. If yous know the side of the rhombus and the value of certain angles, so you can determine the length of the diagonal.

What Does a Rhombus Look Like?

A rhomb is a diamond-shaped quadrilateral that has all four sides equal. We can encounter rhomb-shaped figures in our solar day-to-twenty-four hour period lives. Some of the real-life examples of a rhomb are shown in the below-given figure: a diamond, a kite, an earring, etc.

Rhombus Formulas

The formulae for rhombuses are divers for two attributes:

1. Area of a rhombus, A = 1/two × d₁ × d_two, where d_ane and d_ii are diagonals of a rhomb.
2. The perimeter of a rhombus, P = four × a, where a is the side.

Area and Perimeter of a Rhombus

The area of a rhomb can exist defined as the corporeality of space enclosed or encompassed by a rhombus in a two-dimensional plane. It is half of the product of the lengths of the diagonals. And then, A = 1/2 × d₁ × d_two , where d_i and d_ii are the lengths of the diagonals.

Just like a square, all four sides of a rhombus are equal, and then, the formula for the perimeter of the rhombus is the product of the length of one side by 4. We get P = (4 × a) units, where a is the side of a rhombus.

☛ Of import Notes on Rhombus

Here is a list of a few points that should be remembered while studying about rhombus:

• Next angles in a rhombus are supplementary, they sum upwards to 180°.
• Diagonals bisect each other at right angles.
• All squares are rhombuses, simply not all rhombuses are squares.

☛ Related Topics:

Check out these interesting articles to acquire more about the rhombus and its related topics.

• Rhombus Area Calculator
• Rhombus Worksheets
• Difference Betwixt Kite and Rhombus

Rhombus Examples

1. Example 1: David has drawn a rhombus where the lengths of the two diagonals d_one and d₂ are 5 units and ten units, respectively. He asks his sister Linda to assist him find the area. Can you aid Linda find the reply?

   Solution:

   Given:

   Diagonal, d₁ = 5 units, and d₂ = x units

   A = (d_i × d_two)/two

   A = (5×x)/2

   A = 25 sq. units

   Answer: The area of the rhombus = 25 sq. units.

2. Example 2: Elsa was given the area of a rhombus, 100 square units, and the length of one diagonal as xx units. Can yous assistance Elsa discover the length of the other diagonal?

   Solution:

   Given:

   Area = 100 sq. units, and diagonal d₁ = 20 units

   A = (d₁ × d₂)/2

   100 = (20 × d_two)/ two

   d_ii = x units

   Answer: The length of the other diagonal is 10 units.

3. Example iii: Sam and Victor were playing a game of hopscotch and they spotted a rhombus-shaped tile at the playground. The length of each side of the tile was 15 units. Can yous help Sam and Victor detect the perimeter of the tile?

   Solution:

   Given:

   Length of the tile = 15 units.

   Since all sides of a rhombus are equal, all 4 sides are equal to 15 units.

   Perimeter = 4 × side = iv × 15 = threescore units

   Answer: The perimeter of the tile = 60 units.

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Practice Questions on Rhombus

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FAQs on Rhomb

What is Rhomb in Geometry?

A rhomb is a 2-D shape with four sides hence termed as a quadrilateral. It has two diagonals that bisect each other at correct angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.

Are All Squares Rhombuses?

Yes, all squares are rhombuses. A square tin can be considered equally a special instance of a rhomb considering it has 4 equal-length sides. All the angles of a square are correct angles, but the angles of a rhombus need not necessarily have to be right angles. Hence a rhombus with right angles tin can be considered a square.

What Shape is a Rhombus?

A rhombus is a diamond-shaped quadrilateral. If you lot look at a pack of cards and pull out the xiii diamond cards, yous will find that the diamond geometric shape is that of a rhombus. Information technology has all 4 sides equal and reverse sides parallel to each other. Information technology looks like a tilted square.

Is a Rhombus a Regular Polygon?

No, a rhombus is not a regular polygon. A regular polygon must be equiangular (all of its angles are the same measure) and congruent or, equilateral (all of its sides are the same length). Simply a rhombus is only equilateral: all of its sides are of the aforementioned length and only the opposite angles are equal. A rhomb tin never be considered a regular polygon equally information technology is but an equilateral polygon and non an equiangular polygon.

What is the Area of a Rhombus?

The surface area of a rhomb is calculated by dividing the product of the diagonals by 2. Mathematically, this can be divers as: \(A = \frac{{d_1 d_2 }}{2}\), where d_one and d₂ are the diagonals of a rhomb.

What are the Iv Properties of a Rhombus?

A rhombus is a quadrilateral that has the post-obit four backdrop:

• Opposite angles are ever equal.
• All sides are equal and opposite sides are parallel to each other.
• Diagonals bisect each other at a 90-degree bending and at equal lengths.
• The sum of any two adjacent angles will ever exist supplementary 180°.

What is the Departure Betwixt Rhombus and a Square?

The principal difference between a rhombus and a square is that the angles of a rhombus are not equal to xc° whereas all the angles of a square are equal to ninety°. Information technology is often said that a square is a rhombus, but a rhomb isn't e'er a foursquare.

What is the Difference Between a Parallelogram and a Rhomb?

The divergence between a parallelogram and a rhombus is that in a rhombus all four sides are equal in measurement, whereas a parallelogram has contrary sides equal.

What are the Basic Rhombus Formulas?

A few basic rhombus formulas are listed below:

• Expanse of the rhombus = 1/2 × d₁ × d_two square units.
• The perimeter of a rhombus = (4 × side) units.

What is the Sum of the Interior Angles in a Rhombus?

The sum of the interior angles in a rhomb is 360°.

Are All Angles of a Rhombus 90°?

No, the angles of a rhombus demand not necessarily have to exist correct angles. A rhomb with all iv interior angles as 90-degree angles is considered a foursquare.

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Source: https://www.cuemath.com/geometry/rhombus/