The length of a rectangle exceeds its breadth by $3 \, cm$. If the numerical values of the area and the perimeter of the rectangle are equal,then the breadth is ...... $cm$.

The area of a rhombus is $150 \, cm^2$. The length of one of its diagonals is $10 \, cm$. The length of the other diagonal is ....... $cm$.

If the height of an equilateral triangle is $2 \sqrt{3} \text{ cm}$,then the length of its side is ...... $\text{cm}$.

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

If the length and breadth of a rectangular plot are increased by $50 \%$ and $20 \%$ respectively,then how many times will its area be increased?

An oblong piece of ground measures $19$ $meters$ $2.5$ $dm$ by $12$ $meters$ $5$ $dm$. From the centre of each side,a path $2$ $meters$ wide goes across to the centre of the opposite side. Find the cost of paving these paths at the rate of $Rs.$ $12.32$ per $sq$ $meter$. (in $Rs.$)