In a class, the teacher gave two simiar cardboard pieces which are in the shape of parallelogram to two groups. First group was asked find area of parallelogram,having AB as base. Another group was asked to find the height (h) of parallelogram having AD as base.
What values are depicted?

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Find the area of the parallelogram having two adjacent sides OA and OB where O is the origin and the position vectors of A and B are respectively vec a= hat i+ 2 hat j+ 3 hat k , vec b= -3 hat i- 2 hat j+ hat k .

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases ? If so, why do the vessels filled with water to thatsame height give different readings on a weighing scale ?

Two vessels have the same base area but different shapes. the first vessel takes twice the volume of water than the second, vessel requires to fill upto a particular common height. Is the force exerted by water on the base of the vessel the same in the two cases? If so, why do the vessel filled with water to that same height give differnt readings on a weighing scale?