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All rhombus are parallelogram.

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Important Questions on Quadrilaterals

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The lengths of two diagonals of a rhombus are 10 cm and 24 cm. What is the area (in cm2) of the rhombus?
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The diagonals of a rhombus are of length 20 cm and 48 cm. What is the length of a side of the rhombus?
 
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A wire is in the form of a circle of radius 70 cm. If it is bent in the form of rhombus, then what is its side length?Take π=227
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The diagonals of a rhombus are 15 m and 20 m long. Find its area. 
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The sum of the squares of the sides of a rhombus is 1600 cm2. What is the side of the rhombus?
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In the given figure, ABCD is a rhombus in which c=60°, then AC:BD will be

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One diagonal of a rhombus is 83 cm. If the other diagonal is equal to its side, then the area (in cm2) of the rhombus is:
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A rectangle with 12 cm and 4 cm, reformed into a Rhombus. Both diagonals of Rhombus are equal and one of its angle is 60o. Find the Area of Newly formed Rhombus.

MEDIUM
The diagonals of a rhombus are 32 cm and 60 cm. What is the perimeter of the rhombus?
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The sides of a rhombus are 5 cm each and one diagonal is 8 cm. If the area of the rhombus is k cm2, then find the value of k.

MEDIUM
ABCD is a rhombus. Show that diagonal AC bisects A as well as C and diagonal BD bisects B as well as D
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The area of a rhombus is 84 m2 and length of one diagonal is 24 m. Find the side of the rhombus.
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Diagonal AC of a parallelogram ABCD bisects A. Show that ABCD is a rhombus.
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The area of a rhombus is 119 cm2 and its perimeter is 56 cm. If its height is k cm, then find the value of k.
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The sides of a rhombus are 5 cm each and one diagonal is 8 cm. If the length of the other diagonal is k cm, find the value of k.

EASY
In a quadrilateral ABCD, if AB=BC and CD=DA, then the quadrilateral is a rhombus.
MEDIUM

PQRS is a rhombus:

It is given that PQ=3 cm, if the perimeter of PQRS is k cm, then find the value of k.

HARD
A rectangle having 10 cm and 6 cm as its dimensions was reconstructed to make a rhombus having the same perimeter as that of the rectangle and 60° as one of its angles. The area of rhombus in cm2 was: 
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Diagonals of a parallelogram intersect each other at point O. If AO= 5, BO=12 and AB=13 then, show that quadrilateral ABCD is a rhombus.

MEDIUM
The length of one side of a rhombus is 61 cm and its area is 1320 cm2. Find the sum of length of its diagonals.