Polygons and Area
Section 10-1
A
polygon that is both
equilateral and
equiangular
If
all of the diagonals
lie in the interior of
the figure, then the
polygon is convex.
If
any point of a
diagonal lies outside of
the figure, then the
polygon is concave.
Section 10-2
If
a convex polygon has
n sides, then the sum
of the measures of its
interior angles is
(n-2)180
In
any convex polygon,
the sum of the
measures of the
exterior angles, one at
each vertex, is 360.
Section 10-3
For
any polygon and a
given unit of measure,
there is a unique
number A called the
measure of the area of
the polygon
Congruent
polygons
have equal areas
The
area of a given
polygon equals the sum
of the areas of the
nonoverlapping
polygons that form the
given polygon.
Section 10-4
If
a triangle has an
area of A square units,
a base of b units, and a
corresponding altitude
of h units, then
A = ½ bh
If
a trapezoid has an
area of A square units,
bases of b1 and b2
units, and an altitude
of h units, then
A = ½ h(b1 +b2)
Section 10-5
A
point in the interior
of a regular polygon
that is equidistant from
all vertices
A
segment that is
drawn from the center
that is perpendicular to
a side of the regular
polygon
If
a regular polygon has
an area of A square
units, and apothem of a
units, and a perimeter
of P units, then
A = ½ aP
All
digits that are not
zeros and any zero that
is between two
significant digits
Significant digits
represent the precision
of a measurement
Section 10-6
If
you can draw a line
down the middle of a
figure and each half is
a mirror image of the
other, it has symmetry
If
you can draw this
line, the figure is said
to have line symmetry
The line itself is called
the line of symmetry
If
a figure can be turned
or rotated less than 360°
about a fixed point so that
the figure looks exactly as
it does in its original
position, it has rotational
or turn symmetry
Section 10-7
A
tiled pattern formed
by repeating figures to
fill a plane without
gaps or overlaps
When
one type of
regular polygon is used
to form a pattern
If
two or more regular
polygons are used in
the same order at
every vertex