Explanation:
A circle is a simple shape of Euclidean
geometry consisting of the set of points in a plane that is a given distance from a given
point, the centre. The distance between any of the points and the centre is
called the radius.
Circles are simple closed curves which divide the plane into two regions: an interior and an exterior. In everyday use, the
term "circle" may be used interchangeably to refer to either the
boundary of the figure, or to the whole figure including its interior; in
strict technical usage, the circle is the former and the latter is called a disk.
A circle is a special ellipse in which the two foci are
coincident and the eccentricity is 0. Circles are conic sections attained when a right circular cone is intersected by a plane perpendicular
to the axis of the cone.
Area enclosed
Area
of the circle = π x
area of the shaded square
As proved by Archimedes, the area
enclosed by a circle is equal to
that of a right triangle whose base has the length of the circle's
circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared:
(Our solved example in
mathguru.com uses this concept).
Equivalently, denoting diameter by d,
that is, approximately 79 percent of the circumscribing square (whose side is of length d).
The circle is the plane curve enclosing the maximum area for a
given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality.
http://en.wikipedia.org/wiki/Circle
Rectangle
In Euclidean plane
geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a
non-square rectangle. A rectangle
with vertices ABCD would be denoted as ABCD.
A so-called crossed
rectangle is a crossed
(self-intersecting) quadrilateral which consists of two opposite sides of a
rectangle along with the two diagonals. Its
angles are not right angles. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles
with opposite sides equal in length and equal angles that are not right angles.
If a rectangle has length l and width w
It has area A = lw (Our solved example in mathguru.com
uses this concept).
http://en.wikipedia.org/wiki/Rectangle
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.