Answer to Question #233012 in Geometry for Luuh

Question

To practically clarify the characteristics of investigation; develop teaching and learning activity to investigate the relationship between perimeter ad area of a rectangle

Answer 1

                                           

A rectangle is defined as a polygon with four sides. The opposite sides are equal. All the side angles are at 90⁰ degree. Also, the diagonals bisect each other. 

 

In the above figure, ABCD is a rectangle.

Sides AB = CD = x (say)                  and             AD = BC = y (say)

All the side angles i.e.

$\angle A = \angle B = \angle C = \angle D = 90$⁰

The perimeter is given by: P = AB = BC + CD + DA

Or P = x + y + x + y = 2(x+y)

Area is given by:  A = AB * CD = x*y

Therefore,

Perimeter P = 2(x+y)               and Area A = x*y

Therefore, There is no direct relationship between area and perimeter of a rectangle.