The difference of the areas of two squares drawn on two line segments of different lengths is $32 \, cm^2$. Find the length of the greater line segment if one is longer than the other by $2 \, cm$. (in $cm$)

The area of a big rectangle is equal to the area of a small rectangle. If the length of the big rectangle is equal to the length of the small rectangle and the width of the big rectangle is $2 \ m$,what is the width of the small rectangle?

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)

$A$ circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is $44\, m$,then find the width of the road in $m$.

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?

The sides of a triangle are in the ratio of $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$. If the perimeter is $52 \text{ cm}$,then the length of the smallest side is ........ $\text{cm}$.