A Rhombus Is A Kite

What is Rhombus?

Rhombus is a quadrilateral with all equal sides. Since opposite sides of a parallelogram are equal so, rhombus is a special type of a parallelogram whose all sides are equal.

How is a Rhombus Dissimilar from a Square?

The deviation betwixt a square and a rhombus is that all angles of a square are right angles, just the angles of a rhombus demand not exist correct angles.

And then, a rhombus with right angles becomes a foursquare.

Nosotros can say, "Every foursquare is a rhombus but all rhombus are non squares."

Real-life Examples

Rhomb can be found in a variety of things around usa, such equally finger rings, rhombus-shaped earring, the structure of a window glass pane, etc.

Backdrop of a Rhombus

Some of the properties of a rhombus are stated beneath.

All sides of a rhombus are equal. Here, AB = BC = CD = DA.
Diagonals bisect each other at 90°. Here, diagonals AC and BD bisect each other at 90°.
Opposite sides are parallel in a rhomb. Here, AB ∥ CD and AD ∥ BC.
Opposite angles are equal in a rhombus. ∠A = ∠C and ∠B = ∠D.
Adjacent angles add up to 180°.

∠A + ∠B = 180°

∠B + ∠C = 180°

∠C + ∠D = 180°

∠A + ∠D = 180°

All the interior angles of a rhombus add upwardly to 360°.
Adjacent angles of a rhomb add upwards to 180°.
The diagonals of a rhombus are perpendicular to each other. Here, AC ⟂ BD.
The diagonals of a rhombus bisect each other. Here, DI = BI and AI = CI.
A rhombus has rotational symmetry of 180 degrees (society 2). That is, a rhomb retains its original orientation when rotated by an bending 180 degrees.
The diagonals of a rhomb are the only 2 lines of symmetry that a rhombus has. These separate the rhombus into 2 identical halves.

Surface area of a Rhombus

The area of a rhombus is the region enclosed by the iv sides of a rhombus.

There are ii ways to find the area of a rhomb.

Surface area of a Rhombus When its Base of operations and Altitude are Known

Area of rhombus is calculated by finding the product of its base and corresponding altitude (summit).

And so, Expanse of rhombus = base × height = (b × h) foursquare units.

Area of a Rhombus When its Diagonals are Known

Area of a Rhombus When diagonals are Known

When length of the diagonals of a rhombus are known, then its area is given by one-half of their product.

And so, Area of rhombus = $\frac{(d1\times d2)}{2}$ square units; where d1 and d2 are the diagonals of a rhombus.

Perimeter of Rhombus

The perimeter of a rhomb is the total length of its boundaries. As all the four sides of a rhomb are equal, its perimeter is calculated by multiplying the length of its side by 4.

That is, Perimeter of a rhombus = iv × a units; where 'a' is the length of the side of the rhombus.

Solved Examples:

Example 1: The length of two diagonals of rhombus are 18 cm and 12 cm. Find the expanse of rhomb.

Solution:

Diagonal (d1) = eighteen cm

Diagonal (d2) = 12 cm

Surface area of rhomb = $\frac{(d1\times d2)}{2}$ = $\frac{(xviii\times 12)}{2}$ sq.cm = 108 sq.cm

Example 2: Find the perimeter of the rhombus with its side measuring 15 cm.

Solution:

Length of side of rhombus (a) = 15 cm

Perimeter of rhombus = iv × a = 4 × 15 cm = lx cm

Instance three: The area of a rhomb is 56 sq. cm. If the length of i of its diagonals is 14 cm, find the length of the other diagonal.

Solution:

Area of rhomb = 56 sq.cm

d1 = fourteen cm

We know, area of rhomb = $\frac{(d1+d2)}{2}$

⇒ 56 = $\frac{(14\times d2)}{2}$

⇒ 56 = 7 × d2

⇒ d2 = 56 ÷ 7

⇒ d2 = 8 cm

Then, the second diagonal of the given rhombus measures 8 cm.

Example 4: In rhombus, ABCD, if ∠A = threescore°, detect the mensurate of all other angles.

Solution:

∠A + ∠B = 180° (Adjacent angles adds up to 180°)

60° + ∠B = 180° (Given, ∠A = threescore°)

∠B = 180° – lx°

∠B = 120°

∠C = ∠A = 60° (Opposite angles are equal in a rhombus)

∠D = ∠B = 120° (Reverse angles are equal in a rhomb)

Do Problems

Rhomb

Attend this Quiz & Test your knowledge.

Trapezium

Rectangle

Square

Parallelogram

Correct answer is: Square
All sides of a square are equal, so all squares are rhombus.

5 cm

ten cm

xx cm

40 cm

Right answer is: 10 cm
All sides of the rhombus are equal in length.

4 cm

6 cm

eight cm

ten cm

Correct reply is: eight cm
Expanse = base of operations × distance
⇒ 320 = 40 × distance
⇒ distance = 320 ÷ 40 = 8 cm

500

chiliad

5000

Correct respond is: thousand
Expanse of floor = 500,000 sq. cm
Expanse of each tile = $\frac{(d1\times d2)}{2}$ = $\frac{xl\times 25}{2}$ = 500 sq. cm
Number of tiles = Area of floor ÷ Surface area of 1 tile
= 500,000 ÷ 500
= 1,000 tiles
And so, 1,000 tiles are required to cover the floor.

Frequently Asked Questions

What are the basic properties of a rhombus?

All sides are equal in length.
Opposite angles are equal in a rhomb.
The diagonals bisect each other at xc degrees.
Side by side angles add up to 180 degrees.

Is rhombus a regular polygon?

No, rhombus is not a regular polygon. A regular polygon must have the mensurate of all its angles the same (equal).

The diagonals of rhombus carve up the shape into which shapes?

The ii diagonals of a rhombus form 4 right-angled triangles.

Is a kite shaped similar a rhombus?

No, a kite shape is not a rhomb. Rhombus has all its sides of equal length whereas kite 2 pairs of equal adjacent sides.