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 $\text{cm}$)

Find the area of a triangle in which base is $1.5\, m$ and height is $75\, cm$? (in $sq. cm.$)

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?

In a quadrilateral $ABCD$,the sides $AB, BC, CD, DA$ measure $20\, m, 13\, m, 17\, m$ and $10\, m$ respectively,and the diagonal $AC$ is $21\, m$. The area of the quadrilateral is ........ $m^2$.

In the given figure,$ABCD$ is a square of side $14 \ cm$. $E$ and $F$ are mid-points of sides $AB$ and $DC$ respectively. $EPF$ is a semicircle whose diameter is $EF$. $LMNO$ is a square. What is the area (in $cm^2$) of the shaded region?

The length of a plot is double its width. If a square piece of land of area $150 \, m^2$ occupies $\frac{1}{3}$ area of the plot,then what is the length of the plot? (in $m$)