MEDIUM
Earn 100

 Show that the diagonals of a rhombus divide it into four congruent triangles.

Important Questions on Quadrilaterals

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In the figure given below, a rectangle of perimeter 76 units is divided into 7 congruent rectangles:

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What is the perimeter of each of the smaller rectangles?

EASY
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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How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set 1, 3, 4, 5, 6 ?
EASY

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What is the area of this trapezoidal garden (All measurements are in cm)? 

1. 60 sq.cm
2. 180 sq.cm
3. 210 sq.cm 
4. 240 sq.cm

EASY
The sum of the squares of the sides of a rhombus is 1600 cm2. What is the side of the rhombus?
HARD
Let ABCD be a trapezium, in which AB is parallel to CD, AB=11, BC=4, CD=6 and DA=3 . The distance between AB and CD is
EASY
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 length and breadth of a rectangle are in the ratio 11 : 4. If the perimeter of the rectangle is 300 cm, then what is the length (in cm.) of the rectangle?
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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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The diagonals of a rhombus are 15 m and 20 m long. Find its area. 
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5 : 18 is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

EASY
The lengths of two diagonals of a rhombus are 10 cm and 24 cm. What is the area (in cm2) of the rhombus?
EASY
Three acute angles of a quadrilateral are 82° each. Find out the fourth angle. 
HARD
Let ABCD be a trapezium with AD parallel to BC. Assume there is a point M in the interior of the segment BC such that AB=AM and DC=DM. Then, the ratio of the area of the trapezium to the area of ΔAMD is
MEDIUM
If angles of a quadrilateral are in the ratio 3:5:9:13, find the largest angle.
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Suppose ABCD is a trapezium whose sides and height are integers and AB is parallel to CD. If the area of ABCD is 12 and the sides are distinct, then |AB-CD| is 
 
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All the vertices of a rectangle are of the form (a, b) with a, b integers satisfying the equation (a-8)2-(b-7)2=5. Then, the perimeter of the rectangle is
EASY
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:
MEDIUM

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?