EASY
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All trapeziums are parallelograms.

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Important Questions on Quadrilaterals

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
In a trapezium ABCD, AB is parallel to DC. The diagonals AC and BD intersect at P. If AP:PC=4:(4x-4) and BP:PD=(2x-1):(2x+4), then what is the value of x?
MEDIUM

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?

MEDIUM
How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set 1, 3, 4, 5, 6 ?
MEDIUM
In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to 30. In order to maximize the area of the trapezium, the smallest angle should be:
MEDIUM

5 : 18 is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

MEDIUM
ABCD is a trapezium in which AB is parallel to DC and 2AB=3DC. The diagonals AC and BD intersect at O. What is the ratio of the area of triangle AOB to that of triangle DOC?
MEDIUM
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?
MEDIUM
ABCD is a trapezium in which ABDCAB=50 cm, BC=20 cm, AD=1 cm and the difference between (in cmDC and AB is a whole number. Find the area of the trapezium.
MEDIUM

The accompanying figure shows a right + trapezoid ADBC Based on this information and the information in the figure, the area of the trapezoid (in m2) is 

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EASY
Three acute angles of a quadrilateral are 82° each. Find out the fourth angle. 
MEDIUM
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 
 
MEDIUM
If angles of a quadrilateral are in the ratio 3:5:9:13, find the largest angle.
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

MEDIUM
The diagonals of a rhombus are 32 cm and 60 cm. What is the perimeter of the rhombus?
MEDIUM
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
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 lengths of parallel sides of a trapezium are 60 m and 80 m respectively. If the distance of its parallel sides is 20 m, find the area of the trapezium
EASY
In trapezium ABCDDCABAB=12 cm and DC=7.2 cm. What is the length of the line segment joining the mid points of its diagonals?
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