A floral design on a floor is made up of $16$ tiles which are triangular, the sides of the triangle being $9 \mathrm{cm}, 28 \mathrm{cm}$ and $35 \mathrm{cm}$ as shown in the given figure. Find the cost of polishing the tiles, at the rate of $50$ paise per ${\mathrm{cm}}^2$.

An umbrella is made by stitching $10$ triangular pieces of cloth of two different colours as shown in the given figure, each piece measuring $20 \mathrm{cm}, 50 \mathrm{cm}$ and $50 \mathrm{cm}$. How much cloth of each colour is required for the umbrella?

Find the area of a triangle with base $8 \mathrm{cm}$ and height $5.5 \mathrm{cm}$ (in ${\mathrm{cm}}^2$).

If one side of a parallelogram is $8 \mathrm{cm}$ and its corresponding altitude is $6 \mathrm{cm}$, then find its area.

If the diagonals of a rhombus are $10 \mathrm{cm}$ and $8 \mathrm{cm}$, then find its area.

If the area of an equilateral triangle is $25\sqrt{3} {\mathrm{cm}}^2$, then find the perimeter of the triangle.

If the side of a rhombus is $10 \mathrm{cm}$ and one diagonal is $12 \mathrm{cm}$, then find the area of the rhombus (in ${\mathrm{cm}}^2$).

If the area of an isosceles right-angled triangle is $12.5 {\mathrm{cm}}^2$, then find the length of its hypotenuse.

If the altitude of an equilateral triangle is $\sqrt{6} \mathrm{cm}$, then find its area.