最新SAT数学常识讲解：多边形[1]

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A polygon is a two-dimensional figure with three or more straight sides. (So triangles are actually a type of polygon.) Polygons are named according to the number of sides they have.
　　

　　All polygons, no matter how many sides they possess, share certain characteristics:
　　The sum of the interior angles of a polygon with n sides is (n – 2)

. For instance, the sum of the interior angles of an octagon is (8 – 2)

= 6

=

.

　　The sum of the exterior angles of any polygon is

.

　　The perimeter of a polygon is the sum of the lengths of its sides. The perimeter of the hexagon below is 5 + 4 + 3 + 8 + 6 + 9 = 35.
　　

　　Regular Polygons
　　The polygon whose perimeter you just calculated was an irregular polygon. But most of the polygons on the SAT are regular: Their sides are of equal length and their angles congruent. Neither of these conditions can exist without the other. If the sides are all equal, the angles will all be congruent, and vice versa. In the diagram below, you’ll see, from left to right, a regular pentagon, a regular octagon, and a square (also known as a regular quadrilateral):
　　

　　Quadrilaterals
　　Good news: Most polygons on the SAT have just four sides. You won’t have to tangle with any dodecahedrons on the SAT you take. But this silver cloud actually has a dark lining: There are five different types of quadrilaterals that pop up on the test. These five quadrilaterals are trapezoids, parallelograms, rectangles, rhombuses, and squares.
　　Trapezoids
　　A trapezoid may sound like a new Star Wars character. Certainly, it would be less annoying than Jar Jar Binks. But it’s actually the name of a quadrilateral with one pair of parallel sides and one pair of nonparallel sides.
　　

　　In this trapezoid, AB is parallel to CD (shown by the arrow marks), whereas AC and BD are not parallel.
　　The formula for the aSAT