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 

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

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

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

A rectangle with $12 \mathrm{cm}$ and $4 \mathrm{cm}$, reformed into a Rhombus. Both diagonals of Rhombus are equal and one of its angle is ${60}^{\mathrm{o}}$. Find the Area of Newly formed Rhombus.

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% 

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

What is the perimeter of each of the smaller rectangles?