Geometry
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 so-and-so?” or “What is the perimeter of polygon blah-de-blah?” 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 four-sided 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 45-45-90 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 n-sided 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 seven-sided 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.
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