Question

If the areas of two given shapes are equal, will their perimeters also be equal?

Answer 1

No, it is not necessary that their perimeters are also equal.
For example -
Area of the 1st figure = 6 x 2 $m^2$ = 12 $m^2$
Perimeter of the 1st figure = 6 + 2 + 6 + 2 m = 16 m

Area of the 2nd figure = 4 x 3 $m^2$ = 12 $m^2$
Perimeter of the 2nd figure = 4 + 3 + 4 + 3 m = 14 m

The areas of both these rectangles is same, but their perimeters are different.