The radius and vertical height of a cone are $5 \text{ cm}$ and $12 \text{ cm}$ respectively. Then its lateral surface area is? (in $\text{cm}^2$)

The length of a ladder exactly equals the height of a wall. If the ladder is placed on a $2$-feet tall stool placed $10$ feet away from the wall,its tip just touches the top of the wall. The height of the wall in feet is

$A$ circular swimming pool is surrounded by a concrete wall $4 \ m$ wide. If the area of the concrete wall surrounding the pool is $11/25$ that of the pool,then the radius (in $m$) of the pool is

One of the diagonals of a rhombus is double the other diagonal. Its area is $25\, cm^{2}$. The sum of the diagonals is.......$cm$

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