November 2009
Beginner
368 pages
8h 55m
English
Content preview from Head First 2D Geometry
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306 Chapter 7
circumradius and apothem
The circles give us the properties we need
The base of each triangle in the polygon is the same as one side of
the polygon, and the height and other two sides of the triangle are
radii of the circles inscribing and circumscribing the polygon. The
radius of the circumcircle (goes around the outside) of a polygon is
the polygon’s circumradius, and the radius of the incircle (goes
around the inside) is called the polygon’s apothem.
Circumcircle
Incircle
Around the
outside, through
every vertice
Around the inside,
touching every
side just once
Radius of the
incircle
Radius of the
circumcircle
Radii is just the
plural of radius.
Now we have everything we need
to find the formula of the area
of a polygon, so we can pick the
perfect hot tub. No time to lose!
Circumradius
Apothem
Meets the side
at a right angle
Base
Circumradius
Base
Apothem
The whole
polygon
One triangle
sector
…and the circumradius
is the length of the
other two sides.
The apothem is
the height of the
triangle…
you are here 4 307
regular polygons
(Hint: it looks a lot like one of the intermediate
stages of the circle area formula!)
Area of one triangle ‘sector’ =
×
× ×
×
×
Total area =
Perimeter =
Total area =
number of sides
number of sides
apothem
apothem
apothem
side length
side length
perimeter
side length ...
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