Area of rhombus :
Here we are going to see the formula to be used to find area of rhombus and some example problems.
A quadrilateral which is having four equal sides is called rhombus. In other words a parallelogram will become rhombus if the diagonals are perpendicular.
Area of rhombus = (1/2) x (d₁ x d₂)
Here d₁ and d₂ are diagonals.
SquareEach corner is measuring 90°. Lengths of diagonals are equal. The midpoint of diagonals of square are not equal |
RhombusEach corner is not measuring 90°. Lengths of diagonals are not equal. The midpoint of diagonals of rhombus are equal |
Example 1 :
Find the area of rhombus if the diagonal is measuring 15 cm and 10 cm.
Solution :
Here d₁ = 15 cm d₂ = 10 cm
Area of the rhombus = (1/2) x (d₁ x d₂)
= (1/2) x 15 x 10
= 15 x 5
= 75 cm²
Example 2 :
Find the area of the rhombus whose vertices are A (2,-3), B (6,5), C (-2,1) and D (-6,-7).
Solution :
To find the area 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
= √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 ==> √12 x 12 x 2 ==> 2√12
Area of the rhombus = (1/2) x (d₁ x d₂)
d₁ = √41 d₂ = 2√12
= (1/2) x √41 x 2√12
= √41 x √12
= √12 x 41
= √492
= √2 x 2 x 3 x 41
= 2 √123 square units
After having gone through the stuff given above, we hope that the students would have understood "Area of a rhombus"
Apart from the stuff given above, if you want to know more about "Area of a rhombus", please click here.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
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 |
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
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
Trigonometry 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