


Polygons
A polygon is a fancy math name for a closed
figure with three or more sides. A triangle is a polygon, but two
lines crossing each other are not. A square is a polygon, but a
figure in the shape of the letter C isn’t, because it’s
open on the right side. Many of the polygons you’ll encounter will
be regular polygons. These Joe Schmo polygons have
sides of equal lengths and congruent angles.
Whenever you start talking shapes, you need to talk about
area and perimeter. Many items will ask something like, “What is
the area of figure soandso?” or “What is the perimeter of polygon
blahdeblah?” The area of a polygon is all the space
inside the figure, while the perimeter is the distance
around the outer edge of the figure.
Aside from triangles, most of the polygons on the SAT
will be quadrilaterals. A quadrilateral is any polygon
with four sides. Here’s a nifty chart about foursided polygons,
area, and perimeter. Many of these formulas can be found in the
reference portion of the Math test, but it’s better to know them
from memory.
Hidden Figures Inside Polygons
The first three polygons—square, rectangle, parallelogram—are
the big hitters, while the others may only make a guest appearance
on an item or two. In addition to having nifty formulas for area
and perimeter, these polygons also do a good job of hiding other
geometric figures. Put a diagonal inside a rectangle, and it makes
two right triangles. Put a diagonal in a square, and
it makes two 454590 right triangles. You can also chop up a parallelogram
or a trapezoid to get a rectangle flanked by two triangles. Don’t
take our word for it: do it yourself and see.
Interior Angles
Another formula for polygons concerns the sum of the interior
angles. For an nsided polygon, the sum of the
interior angles is found with the formula (n –
2)180 = sum of the interior angles. If you have a triangle, the
sum is: (n – 2)180 = (3 – 2)180 = (1)180 =180,
but you knew that already. For a sevensided heptagon,
the sum is: (n – 2)180 = (7 – 2)180 = (5)180 =
900. You can contrast this formula for interior angles with the
fact that the sum of the exterior angles of any polygon is always
360˚.
Know your polygons. ’Nuff said.
