The cost of papering four walls of a room at ₹ 14 per square metre is ₹ 3,150. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 4 : 1.

A circle is inscribed in a square of side 14 cm. Find the area enclosed between the square and the circle.

Find the ratio between the area of the shaded and the unshaded portions of the following figure :

Calculate the area of a triangle whose sides are 13 cm, 5 cm and 12 cm. Hence, calculate the altitude corresponding to the longest side of this triangle. Leave your answer as a fraction.