Perimeter Formula Of A Rhombus

The perimeter of a Rhombus formula is iv x s (Hither, s = the side length of the rhomb). Rhombus is a flat-shaped ii dimensional structure having four equal angles and four equal sides. The 4 angles are non 90 degrees necessarily.

This shape is as well considered to be a diamond-shaped structure. The perimeter of the rhombus is actually the total distance covered along the border of it.

Central Terms: Rhombus, Perimeter, Pythagoras Theorem, Side by side Angles, Bisect, Diagonals

Perimeter of Rhomb

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According to the definition of the Rhombus,

Perimeter of Rhombus = four ten southward

Where,

southward = the side length of the rhombus.

Hence, P = s + south + due south + due south = 4s

Rhombus

Rhomb

Area of the Rhombus

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The area of rhombus can be adamant in two means:

i) By multiplying the tiptop & base of the rhomb

Area = b x h [b = base of operations of rhomb; h = height of rhombus]

ii) Past determining the product of the diagonal of the rhombus & dividing information technology by two

Expanse = ½ 10 d₁ x d₂[d₁ & d₂ are the diagonals of the rhombus]

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Derivation of the Area of Rhomb

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If MNOP is considered a Rhombus with base MN = b, PN ⊥ MO, MO is a diagonal of rhombus = d_ii; PN is a diagonal of rhombus = d₁; altitude from O on MN is OZ which is = h.

Then, the expanse of the rhombus MNOP = 2 x surface area of ∆ MNO

= 2 x ½ MN 10 OP

= 2 ten ½ b 10 h (sq. Units)

The area of the rhombus = 4 10 Area of ∆ MZP

= 4 x ½ ten MZ ten ZN

= 4 x ½ 10 d₂ ten ½ d_ane (sq. Units)

= 4 x 1/8 d_ane x d₂

The area of a rhombus = ½ x d₁ x d₂

Finding Perimeter of Rhombus Using Diagonal Lengths

Given, in a rhombus PQRS, a as the horizontal diagonal length and b every bit vertical diagonal length and centre o.

Let's take triangle POS, and then the length of
OP = a/2

Bone = b/2

If we assume the side of the rhomb every bit = X

Using Pythagoras theorem,

Ten² = a^two/two + b²/2

X² = (a² + bⁱⁱ)/4

X = \(\sqrt{ \frac{( a^two+b^2)}{ii}}\)

Past substituting the value of X in the rhombus formula = 4X, nosotros go,

4 x \(\sqrt{ \frac{( a^2+b^two)}{2}}\)

So, the perimeter will be = 2 ten \(\sqrt{ \frac{( a^2+b^2)}{2}}\)

Properties of Rhombus

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Rhomb is known to be a square due to the post-obit properties of Rhomb:

It's all sides have equal length
Information technology's opposite sides are parallel
Its diagonals bisect each other at xc degrees.
Two adjacent angles forms a total of 180 degree
Information technology's altitude is the altitude at right angles between the two parallel sides

Things to Call back

Diagonals of a rhomb carve up each other at right angles or 90 degrees.
The perimeter of a rhombus is said to be the sum of all four sides
The sum of all the angles of a rhombus is 360 degrees
The rhomb share the aforementioned backdrop equally that of a foursquare. Hence, rhombus is likewise said to exist a foursquare.
Rhombus differs from rectangle in a way equally rhomb has opposites angles equally equivalent while rectangle has opposite sides as equivalent

Sample Questions

Ques. What is the perimeter of a rhombus with side 8 cm? (2 marks)

Ans: Given, side of the Rhomb = 8 cm

Perimeter of rhombus = 4 x s

= 4 10 eight cm = 32 cm

Ques. The diagonals of a rhombus are 44 cm and 15 cm. Find the area of the rhombus. (2 marks)

Ans: Permit'southward accept, a = 44 cm; b = 15 cm

Area of the rhomb (A) = ½ x a 10 b

= ½ x 44 cm x xv cm

= 330 cm^two

Ques. The side of a rhombus is ii.5 cm. What is the perimeter of the rhombus? (2 marks)

Ans: Let's take, south = two.5 cm

Perimeter of rhombus (given) = 4 ten s

Hence, (P) = iv x ii.5 cm

= 10 cm

Ques. The diagonals of a rhombus are 24 cm and 10 cm. Observe the area of the rhombus. (2 marks)

Ans: Let's take, a = 24 cm; b = ten cm

Surface area of the rhombus (A) = ½ x a x b

= ½ x 24 cm x 10 cm

= lx cm²

Ques. What is the perimeter of a rhombus with side 16 cm? (2 marks)

Ans: Given, side of the Rhombus, s = 16 cm

Perimeter of rhombus = iv x s

= 4 x 16 cm = 64 cm

Ques. What is the perimeter of a rhomb having ii diagonals of vi cm & 8 cm respectively? (three marks)

Ans: Given, d₁ = 6 cm; d₂ = eight cm

According to the formula,

Perimeter of rhombus = 2 x \(\sqrt{ \frac{( a^two+b^2)}{2}}\)

= 2 x \(\sqrt{ \frac{( 6^2+eight^2}{2}}\)

= two x 10

= twenty cm

Ques. Find the perimeter of a rhomb having two diagonals of 4 cm & 6 cm respectively? (3 marks)

Ans: Given, d₁ = 4 cm; d₂ = 6 cm

According to the formula,

Perimeter of rhombus (P) = 2 10 \(\sqrt{ \frac{( a^two+b^2)}{two}}\)

= 2 x \(\sqrt{ \frac{( 4^2+6^ii}{2}}\)

= 2 ten 5.8 cm

= 11.6 cm

Ques. The Perimeter of a rhombus is 48 cm. Find the side of a rhombus. (3 marks)

Ans: Given, perimeter of the Rhombus (P) = 48cm

Hence, P = iv x s [according to formula]

south = p/four

south = 48/iv cm = 12 cm

So, the side of the rhomb is 12 cm

Ques. Find the perimeter of a rhombus with a given side of v cm. (3 marks)

Ans: Given, side of a rhomb, southward = 5 cm

According to the formula, perimeter of the rhomb is

P = four x s

= 4 ten five cm

= twenty cm

Ques. The perimeter of a rhombus is sixty cm. Find the side of a rhombus. (3 marks)

Ans: Given, perimeter of the Rhombus (P) = 60 cm

Hence, Perimeter of the rhombus, P = 4 x s [according to the formula]

due south = p/4

s = 60/4 cm = fifteen cm

So, the side of the rhombus is 15 cm

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