$ABC$ 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 $ABD$?

The perimeter of a right triangle is $12 \, cm$. The hypotenuse is $5 \, cm$. What are the other two sides and the area of the triangle?

In $\Delta ABC$,$AD$ and $AE$ are bisectors of $\angle BAC$ and $\angle BAD$ respectively. If $\angle BAE = 30^{\circ}$,$AE = 9 \text{ cm}$,and $EC = 15 \text{ cm}$,what is the area (in $\text{cm}^2$) of $\Delta AEC$?

$A$ wire which when bent in the form of a square encloses an area of $484 \, cm^2$. What will be the enclosed area when the same wire is bent into the form of a circle? (in $cm^2$)

If every side of a triangle is doubled,the area of the new triangle is $K$ times the area of the old one. $K$ is equal to

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