$ABCD$ is a trapezium with $AD$ and $BC$ as parallel sides. $E$ is a point on $BC$. The ratio of the area of $ABCD$ to that of $\Delta AED$ is

Height of an equilateral triangle is $6 \, cm$. Find its side? (in $cm$)

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes.

What would be the cost of laying a carpet on a floor which has its length and breadth in the respective ratio of $32:21$ and where its perimeter is $212$ feet,if the cost per square foot of laying the carpet is $₹ 2.5$?

If the two diagonals of a parallelogram are $72 \, cm$ and $30 \, cm$ respectively,then find its perimeter in $cm$.

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?