area of a parallelogram

base times corresponding height (height must be perpendicular to THAT base) (base will always be the actual length of a side, NOT the extended length or the dotted  height)

area of a triangle

½ times base times corresponding height

simplifying radicals

removing perfect square factors from under the radical AND rationalizing the denominator

rationalizing the denominator

multiplying the denominator by a number under a radical, so that the number under the radical is a perfect square, then taking the square root

Pythagorean theorem

hypotenuse squared = a leg squared PLUS the other leg squared  (c² = a² + b²  )

hypotenuse of a right triangle

the side opposite the right angle in the right triangle

leg of a right triangle

either of the sides that form the right angle in the right triangle

45-45-90 triangle formulas

hypotenuse = side * ¸  ;  leg = other leg

short leg of 30-60-90 triangle

leg opposite the 30 degree angle

long leg of 30-60-90 triangle

leg opposite the 60 degree angle

30-60-90 triangle formulas

hypotenuse = 2 * short leg; 

long leg = short leg * ø3  

area of a trapezoid

½ times height times (base₁  + base₂)

height of a trapezoid

the perpendicular distance between the 2 bases

bases of a trapezoid

the parallel sides of a trapezoid (never @)

center of a regular polygon

center of a circle circumscribed around the regular polygon

apothem of a regular polygon

the segment going perpendicularly from a side of the polygon to the center of the polygon

radius of a regular polygon

the segment from the center to a vertex of the regular polygon

area of a regular polygon

½ * apothem*perimeter of the polygon OR form right triangles  using a radius and apothem, find the area of that right triangle (use A = ½ base * corresponding ht).  Multiply that area by 2 * number of sides of the polygon

Circumference of a circle

C = 2 ¹ r   OR  C = ¹ d  EXACT:  Leave in terms of pi.

arc length

part of the circle * Circrumference

degree measure  *2 ¹ r  

     360

concentric circles

circles in the same plane having the same center, but  different radii

area of a circle

¹ r²  

sector of a circle

region bounded by 2 radii and their intersected arc.   (a slice of pie)

area of a sector

part of the circle * area of the circle   OR

degree measure   * ¹ r² 

   360

area of a segment

area of the sector minus the area of the triangle