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quarterarea

Quarterarea is a term used in geometry to denote the area of one quarter of a plane region. It can refer to the area of a subregion obtained by partitioning the region into four congruent parts with two perpendicular lines intersecting at a central point, typically the region’s centroid or center of symmetry. Alternatively, quarterarea can denote the portion of a region that lies within a particular Cartesian quadrant, such as the first quadrant.

Calculation and interpretation: If a region is partitioned into four equal parts, each quarterarea equals one

Examples: The quarter of a circle is one-fourth of its area (πr^2/4). The quarter of a rectangle

Applications: Quarterarea concepts appear in geometric analysis, partition-based algorithms, Monte Carlo sampling, and curriculum examples illustrating

See also: Quadrant, Area, Polygon area, Symmetry.

quarter
of
the
total
area.
For
standard
shapes,
straightforward
formulas
apply:
a
circle
of
radius
r
has
quarterarea
πr^2/4,
a
rectangle
with
sides
a
and
b
has
quarterarea
ab/4,
and
a
square
with
side
s
has
quarterarea
s^2/4.
For
arbitrary
polygons
or
irregular
regions,
quarterarea
is
computed
by
determining
the
total
area
A
and
identifying
the
subregion
that
corresponds
to
the
quarter;
this
may
involve
polygon
clipping,
integration,
or
numerical
methods
if
the
quarters
are
not
equal
by
simple
partition.
is
one-fourth
of
its
area
(ab/4).
In
the
quadrant
interpretation,
quarterarea
is
the
area
of
the
part
of
the
region
that
lies
in
the
chosen
quadrant.
area
division
and
symmetry.