EASY
Earn 100

 A transversal cuts two parallel lines at A and B. The two interior angles at A are bisected and so are the
two interior angles at B;the four bisectors form a quadrilateral ABCD. Prove that ABCD is a rectangle 

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Important Questions on Quadrilaterals

EASY
The perimeter of a rectangle is 28 cm. If the length is 52 times its breadth, find the length and breadth of the rectangle.
EASY
If the perimeter of a certain rectangle is 50 units and its area is 150 sq.units, then how many units is the length of its shorter side?
EASY
The perimeter of a rectangle is 86 cm. The numbers representing its area and breadth are in the ratio of 9:1, respectively. The breadth of the rectangle is:
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 hall is 15 m long and 12 m broad. The sum of the areas of the floor and the ceiling is?(in square meters).
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
EASY
The length of the diagonal of a rectangle is 26 cm and one side is 10 cm.The area of the rectangle is _____.
MEDIUM
The diagonals of a rhombus are 32 cm and 60 cm. What is the perimeter of the rhombus?
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?
HARD

A rectangular garden of length 12 m is surrounded by a 2 m wide path. If the area of the garden is 84 m2 and the cost of gravelling is 8 per m2, then what is the total cost of gravelling the path?

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

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

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

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
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

If the length and breadth of a rectangle are increased by 10% and 70% respectively, the increase in the area of the rectangle will be: 

(A) 87% 

(B) 92% 

(C) 96% 

(D) 95% 

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?