Let the height of the parallelogram = h cm
Then the base of the parallelogram = 3h cm
Area of the parallelogram = 192 sq. cm
b x h = 192
3h x h = 192
3h² = 192
h² = 64
h x h = 8 x 8
h = 8 cm
base = 3h = 3 x 8 = 24 cm
Therefore, base of the parallelogram is 24 cm and height is 8 cm.

Given that the adjacent sides of parallelogram are 12 cm and 9 cm
If we choose the shorter side as base, that is b = 9 cm then distance between the shorter sides is height, that is h = 8 cm
Area of parallelogram = b x h sq.units = 9 x 8 = 72 sq. cm.
Again, if we choose longer side as base, that is b = 12 cm then distance between longer sides is height. Let it be 'h' units.

We know that, the area of the parellelogram = 72 sq.cm
b x h = 72
12 x h = 72
\(h=\cfrac { 72 }{ 12 } =6cm\)
Therefore, the distance between the longer sides = 6 cm.

Given: Area = 368 sq. cm , base b = 23 cm
Area of the parallelogram = 368 sq. cm
b × h = 368
23 × h = 368
\(h=\cfrac { 368 }{ 23 } \)
Thus, the height of the parallelogram = 16 cm.

Given: b = 12 m, h = 8 m
Area of the parallelogram = b x h sq.units
= 12 x 8 = 96 sq.m
Therefore, Area of the parallelogram = 96 sq.m.

(i) From the Fig.2.4
Base of a parallelogram (b) = 15 cm, Height of a parallelogram (h) = 4 cm
Area of a parallelogram = b x h sq.units. Therefore, Area = 15 × 4 = 60 sq. cm.
Thus, area of the parallelogram is 60 sq. cm.
Perimeter of the parallelogram = sum of the length of the four sides.
= (15 + 5 +15 + 5) = 40 cm.
(ii) From the Fig.2.5
Base of a parallelogram (b) = 9 m, Height of a parallelogram (h) = 16 cm.
Area of a parallelogram = b × h sq.units Therefore, Area = 9 × 16 = 144 sq. cm
Thus, area of the parallelogram is 144 sq. cm.
Perimeter of the parallelogram = sum of the length of the four sides.
= (18 + 9 +18 + 9) = 54 cm.