7.7 SAT Math - Polygons

A polygon is simply a shape with 3 or more sides, so triangles are polygons, as are quadrilaterals, as are hexagons, octagons, and any other shape with multiple sides.

Multi-sided polygons aren't tested much on this test, except in two ways.  One is perimeter, in which all you have to do is add up the sides.  The other way asks about the sum of the interior angles.  You know that a triangle adds up to 180° and a quadrilateral to 360°, but what about the other shapes?

There are two ways to solve.  If you're good with memorization, there's a formula you can memorize for the SAT math section: (n - 2)•180, where n is the number of sides in the shape requested.

If you're not good with memorizing, don't worry.  Pick a vertex (a corner) on the shape and draw a line to every other vertex on the shape.  This will create a series of triangles, and from there, you simply count the number of triangles you have and multiply by 180°.  Let's take a look:

4. In the hexagon above, the sum of the interior angles is

(A) 120
(B) 180
(C) 360
(D) 720
(E) 1080

To draw out your answer, pick a vertex and draw lines:

You have four triangles, so multiply by 180 to get 720, or D).

Alternatively, use the formula: (6 -2)•180 = 4•180 = 720.

If you find yourself with strange-shaped polygons and the question is asking you for something more complicated than perimeter or interior angles, take another look.
-Hint: Look for shapes within shapes.  If the shape you've been given is odd, it's probably a triangle inside a circle, or a square inside a triangle.  Split the odd shape into familiar shapes in order to solve:

            -SAT Math Strategy: Measuring.  Here's a strategy the SAT testmakers and your teachers don't want you to know about:  If you are stuck trying to find the length of a side, you do not have to really do the math.  You know the rule about Eliminating Obviously Wrong Answers, which means without much work you should be eliminate two or three choices.  From there, use the edge of the answer sheet as a ruler.  Mark the length of a known side very lightly on your answer sheet.  Compare that length to the length of the side you're looking for and take an educated guess.  You can double-check yourself by measuring another known side and guessing based on that one as well to see if your two guesses match up.  The answer choices are rarely so close apart that a strong guess won't yield the correct answer, but even if you are torn between two choices, pick one and move on.  This is a strategy meant to get you through some of the harder or more puzzling questions, so your chances of getting it right even doing the math aren't much better than 1 in 2, and by Measuring, you save a lot of time and a lot of stress.

-SAT Math Hint: Be sure and mark your 'ruler' extremely lightly and to erase it completely when you are done!  You do not want to have stray pencil marks on your answer sheet that will mess up the grading computer and invalidate your answer sheet!