SECTION 25.1: WHAT ARE "UNITS"?
"Units" or "units of measurements" are labels which distinguish one type of measurable quantity from other types. A number always precedes a "unit." I will deal with units of "length".
The measurable quantity "length" is determined by a
"ruler." See below:
EXAMPLES OF THE DIFFERENT UNITS OF LENGTH
USED IN SENTENCES 
SENTENCE 

UNIT OF LENGTH USED 
John walked 10 miles today 

miles 
Mary is 5 feet tall. 

feet 
Tom bought 6 yards of carpeting for his room. 

yards 
The road from Bangor to Nova Scotia is 540 kilometers long. 

kilometers 

There are numerous units of length: centimeter, millimeter, Angstrom,
inch, etc. Also, there are numerous units having nothing to do with length, e.g.
pounds, degrees centigrade, grams, dollars, etc.
SECTION 25.2 WHAT IS A "PLANE FIGURE"?
I will be speaking in everyday language. The language that I'll use is not
considered precise mathematical language.
Let's consider the concept of a "plane." A "plane" is
a "flat surface." A piece of paper can be thought of as a plane. The
top of a table can be thought of as a plane. An "object" drawn on a "plane" is called a "plane figure."
SECTION 25.3: THE MEANING OF AREA
I am assuming you have a basic understanding of a "square". A "square" is a 4 sided plane figure, i.e. a quadrilateral,
with all sides equal in length and a 90 degree (90°)
angle where the sides intersect.
Consider the following squares:
SECTION 25.4: EXAMPLES OF
AREAS AND THEIR MEANINGS
MEANING OF AREA Z units^{2} 
Z units^{2}
where Z is a real number such that Z ≥ 0
means
The amount of surface on a plane made up of
a)
Z squares
and
b)
the sides of each square has a length of 1 unit.
Comment: The unit could be inches, feet, yards, miles, etc. In effect the unit can be any measurement of length. 
Consider the following examples of areas:
ex. 1) 10
in.^{2}
Pronounced 10 square inches.
Meaning: A surface that contains 10 squares, each square having a side of 1
inch.
Visual
representation:
Comment: I could rearrange the above squares in any way I want and I would still have 10
in.^{2}. I could cut the squares up into thousands of bits and pieces and still have 10 in^{2}.
ex. 2) 20
ft.
Pronounced 20 square feet.
Meaning: A surface that contains 20 squares, each square having a side of 1
foot.
Visual
representation:
ex. 3) The earth has a surface area of 196,940,400
mi.
Pronounced one hundred and ninety six million, nine hundred and forty
thousand, four hundred square miles.
Meaning: A surface that contains 196,940,400 squares, each square having a
side of 1 mile.
Visual representation: Sorry! Too many squares!
ex. 4) The moon has a surface area of 23,000,000
mi.
Pronounced twenty three million square miles.
Meaning: A surface that contains 23,000,000 squares, each square having a side
of 1 mile.
Visual representation: Sorry! Too many squares!
I need to review a few ideas,
SECTION 25.5: WHAT ARE
PARALLEL LINES?
Two lines are "parallel" if they are equally distant
from each other.
SECTION 25.6: WHAT ARE
PERPENDICULAR LINES?
Two straight lines are "perpendicular" if the angle at their
point of intersection is 90
degrees(90°).
SECTION 25.7: HASH MARKS AND ARROWS
HASH MARKS 
Hash marks small line segments and are indicators of sides of plane figures having equal lengths. If the sides of a plane figure are marked with the same number of hash marks then those sides are equal. 
ex. 1)
 Sides bc and ad are
understood to be equal in length because they have the same number of hash
marks: 2 on each side.
 Sides ab and dc are understood to be equal in length because they have the
same number of hash marks: 1 on each side.
ex. 2)
 Sides bc, cd, da, and ab are understood to be equal in length because they
have the same number of hash marks: 1 on each side.
ex.
3)
 sides ab and ac are understood to be equal in length because they have the
same number of hash marks: 3 on each
side.
SECTION 25.8: THE ARROW MARK
FOR PARALLEL LINES
I am assuming that you understand that two lines are parallel when they are
equally distant from each other.
An "arrow mark" is a small arrow placed along a pair line
segments of a plane figure and is used to mark that sides of a plane figure
that are parallel. An arrow mark may have more than one arrowhead.
ex. 1)
 bh is parallel to yj since the sides have the same number of arrow marks: 1
arrow mark on each side.
ex. 2
 zh is parallel to kv since the sides have the same number of arrow marks: 2
arrow marks on each side.
ex. 3)
 tn is parallel to we since the sides have the same number of arrow marks: 3
arrow marks on each side.
 wt is parallel to en since the sides have the same number of arrow marks: 2
arrow marks on each side.
SECTION 25.9: SOME PLANE
FIGURES AND THEIR AREA FORMULAS
Below are some plane figures, their characteristics and their area formulas.
SECTION 25.10: PERIMETER OF A
PLANE FIGURE
EXAMPLES: FIND THE AREA AND PERIMETER OF THE FOLLOWING PLANE FIGURES
ex. 1)
ex. 2)
ex. 3)
ex. 4)
ex. 5)
ex. 6)
