Area of Rhombus

Here we will discuss Area of Rhombus.
As all the sides of rhombus are equal so the perimeter of rhombus is same as that of square.

The diagonals of rhombus bisect each other at right angle.

Perimeter of Rhombus = 4 x side
Area of a rhombus = ½ [ product of the diagonals]
Area = Base x Height

Some solved examples :

1) The side of a rhombus is 18 cm . Find its perimeter.
Solution :
Perimeter of Rhombus = 4 x side
⇒ = 4 x 18
&rArr = 72 cm
∴ Perimeter of Rhombus = 72 cm.
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2) Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.
Solution :
Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12
Let BO = x and AB = 13 cm (given)
By Pythagorean theorem
c
2 = a 2 + b 2
13
2 = 12 2 + x 2 169 = 144 + x 2
x
2 = 169 – 144
x
2 = 25
x = 5 cm
BO = 5 cm
Diagonal BD = 2 x 5 = 10 cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 10
Area = 120 sq.cm

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3) If the area of a rhombus is 24 sq.cm and one of its diagonal is 4 cm find the length of the other diagonal.

Solution :
Area = ½ x d1 x d2
24 = ½ x 4 x d2
24 = 2 x d2
d2 = 24/2
d2 = 12 cm



Mensuration : Area and Perimeter

Perimeter and Area of Irregular Shape
Area and Perimeter of the Rectangle
Area of Square (perimeter of square)
Perimeter of Parallelogram(Area of Parallelogram)
Area of Rhombus(Perimeter of rhombus)
Area of Trapezoid (Trapezium)
Triangle Area (Perimeter of triangle)
Herons Formula

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