PERIMETER OF RHOMBUS
In this page perimeter of rhombus, we are going to see formulas to be used to find the perimeter of the shape rhombus.
Ways to find perimeter of rhombus:
We have three ways to find perimeter of the shape rhombus.
(i) Using side length
(ii) Using length of diagonals
(iii) Using one diagonal and one angle
Perimeter using side length:
In rhombus length of all sides will be equal. So, perimeter of rhombus is nothing but sum of all sides.
Perimeter = a + a + a + a = 4 a
here "a" stand for length of each side.
Perimeter using length of diagonals :
Perimeter = 2 √ d₁² + d₂²
here d₁ and d₂ stands for length of diagonals.
Perimeter using one diagonal and one angle :
Let us see an example problem to understand how to find perimeter of the shape rhombus using one diagonal and one angle.
Example 1:
Find the perimeter of the shape rhombus given below.
Solution :
According to the properties of rhombus
(i) Each diagonals bisect the vertex angle.
(ii) The diagonals of rhombus are perpendicular and they bisect each other.
Here AC = 16 cm
So, AE = 8 cm ∠EAB = 35° and ∠AEB = 90°
In triangle AEB,
AB = hypotenuse side, BE = opposite side and AE = adjacent side
cos θ = Adjacent side/hypotenuse side
cos 35° = AE / AB
0.819 = 8 / AB
AB = 8 / 0.819
= 9.768
perimeter of rhombus ABCD = 4(9.768) = 39.07 cm
Hence, perimeter of rhombus = 39 cm
Example 2:
Find the length of the other diagonal and area of rhombus.If the perimeter of a rhombus is 20 cm and One of the diagonals is of length 8 cm.
Solution:
Since one of the diagonal is given and we have to find the other diagonal. So we have to use the first formula.
Perimeter of the rhombus = 2 √ d₁² + d₂²
Here d₁ = 8 cm
Perimeter of the rhombus = 20 cm
2 √8² + d₂² = 20 ==> √64 + d₂² = 20/2 ==> 64 + d₂² = (10)²
64 + d₂² = 100 ==> d₂² = 36 ==> d₂ = 6 cm
So area of rhombus = (1/2) x 8 x 6
= 4 x 6==> 24 cm²
Example 3:
Find the length of each side of rhombus if the perimeter is measuring 260 cm.
Solution:
Perimeter of the rhombus = 260 cm
4a = 260 m
a = 260/4
a = 65 cm
Example 4:
Find the perimeter of the rhombus whose vertices are A (2,-3), B (6,5), C (-2,1) and D (-6,-7).
Solution:
To find the perimeter of the rhombus first we have to find the length of the diagonals.
Distance between two points = √(x₂ - x₁)² + (y₂ - y₁)²
Length of diagonal AC
A (2,-3) C (-2,1)
x₁ = 2 y₁ = -3
x₂ = -3 y₂ = 1
= √(-3 - 2)² + (1 - (-3))²
= √(-5)² + (1 + 3))²
= √25 + (4))²
= √(25 + 16)
= √41
Length of diagonal BD
B (6,5) D (-6,-7)
x₁ = 6 y₁ = 5
x₂ = -6 y₂ = -7
= √(-6 - 6)² + (-7 - 5)²
= √(12)² + (12)²
= √144 + 144
= √288
Perimeter of rhombus = 2 √ (√41)² + √288)²)
= 2 √ 41 + 288
= 2 √329 cm
More shapes
|
Square  Parallelogram  |
Rectangle  Rhombus |
|
Traingle  Quadrilateral  Sector 
Hollow cylinder  Sphere  Area around circle  Area of combined figures  |
Trapezium Circle  Semicircle  Quadrant  Cyclinder  Cone  Hemisphere  Path ways  |
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
