If the area of a triangle is $150 \, m^{2}$ and the ratio of the base and the height is $3:4$,then find its height in $m$.

Mid-points of a triangle containing sides $12 \, cm$,$18 \, cm$,and $26 \, cm$ are joined to each other. Find the area of the triangle formed by joining the mid-points.

$ABC$ is a triangle. $AB = 5 \text{ cm}$,$AC = \sqrt{41} \text{ cm}$,and $BC = 8 \text{ cm}$. $AD$ is perpendicular to $BC$. What is the area (in $\text{cm}^2$) of triangle $ABD$?

If the area of a triangle with base $x$ is equal to the area of a square with side $x,$ then the altitude of the triangle is

The length of a rectangular plot of land is three times as much as its breadth. $A$ playground measuring $1200 \ ft^2$ occupies $\frac{1}{4}$ of the total area of the plot. What is the length of the plot in feet?

The surface area of a spherical part of a bowl with a flat circular detachable cover,excluding the cover,is $616 \, cm^2$. The area of the cover is $38.5 \, cm^2$. What is the volume of the bowl? (in $cm^3$)