Calculate the area of regions marked $P, Q$ and $R$ in the given rectangle.

The area of a triangle is equal to that of a square whose each side measures $70 \mathrm{cm}$. Find the side of the triangle in metre, corresponding to the altitude measuring $35 \mathrm{cm}$.

Find the area of the shaded region in the figure given alongside.

The area of a rhombus is equal to that of a triangle whose side and the corresponding altitude are $24 \mathrm{cm}$ and $15 \mathrm{cm}$ respectively. If one of the diagonals of the rhombus is $18 \mathrm{cm}$, find the other.

The floor of a hall which is $7.2 \mathrm{m}$ long and $5.8 \mathrm{m}$ wide is to be constructed using square tiles measuring $20 \mathrm{cm}\times 20 \mathrm{cm}$. Find the number of tiles required to cover the floor. Also find the cost of the tiles at the rate of $₹276$ per dozen.

Find the area of the shaded portion in the following figures. Are these areas equal? Why?

A pulley cabin car ferries tourists on a ropeway from the base to the hill top which is $6.28 \mathrm{km}$ away. The rope loops around a giant wheel that is $5 \mathrm{m}$ in diameter. How many revolutions must the giant wheel make to get the tourist on top ?

The altitude of a field in the form of a triangle is half of its base. If the cost of irrigating the field at the rate of $₹280$ per hectare is $₹4480$, find its base and altitude. 

What is the importance of irrigation in agriculture?

A circular wire in the form of a ring is cut and converted into an equilateral triangle of side$44 \mathrm{dm}$. Find the radius of the ring.

What is the importance of minimizing the wastage while using the resources?