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Squares And Rectangles:

A.  Definitions

1.  A square is defined as having 4 sides all of which are equal and whose inside angles are all 90 degrees.

2.  A rectangle is defined as having 4 sides whose inside angles are all 90 degrees.

B.  Basic Memorizations

Square: 

Area = s², where 's' is a side

Area = , where 'd' is the diagonal

Perimeter = 4s

Diagonal =

Rectangle:

Area = , where 'l' is the length and 'w' is the width

Area = , where 'd' is the diagonal

Perimeter =

Diagonal =

C.  Examples

Ex [1]  The perimeter of a square is equally numerical to its area.  Each side is ______ units?

a.  The only way this is true is if 4s = s².  The only way this is possible is for s = 0 or s = 4.  Since a square cannot have a side of 0, the answer is 4.

Ex [2]  If the perimeter of a rectangle is 28 units, and one side is 6 units, then the diagonal measures _____ units.

a.  We know that the perimeter of a rectangle is 2l+2w.  If one side is 6, then this forces the other side to be equal to: 2(6)+2w=28.  Solving for w, we get w=8.

b.  With two sides of 6 and 8, the diagonal is equal to which is 10.  You can see this quickly if you know your Pythagorean Triples.

c.  The answer is 10.

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