If the diameter of each circle is $14 \, cm$ and $DC = CE$,find the area of $\Delta BDE$ in $cm^2$.

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?

$\Delta ABC$ is similar to $\Delta PQR$. The length of $AB$ is $16 \ cm$ and the length of the corresponding side $PQ$ is $9 \ cm$. If the area of $\Delta ABC$ is $1024 \ cm^2$,what is the area of $\Delta PQR$ in $cm^2$?

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter,then $X$ is

What is the radius of a circle,to the nearest $cm$,whose area is equal to the sum of the areas of the three circles of radii $22\, cm$,$19\, cm$,and $8\, cm$ respectively? (in $cm$)

The perimeter of a triangle is $30 \text{ cm}$ and its area is $30 \text{ cm}^2$. If the largest side measures $13 \text{ cm}$,then what is the length of the smallest side of the triangle? (in $\text{cm}$)