Examples: Drop the altitude from B to AC with the foot of the altitude at D. This creates 30-60-90 triangle ABD. AB=4 so AD=2 and BD (the altitude of triangle ABC) = 2√3cm, making the area of triangle ABC: ଵ · ଶ√ଷ ଶ = √. Q1: What is the area in square units of an equilateral triangle with a perimeter of 8 units? Express your answer as a common fraction in simplest radical form. 2. There are 62 possible outcomes for two rolls of a pair of dice. There is one way to roll a 2 (1,1), there are 2 ways to roll a 3, three ways to roll a 4, four ways to roll a 5, five ways o roll a 6, six ways to roll a 7, 5 to roll an 8, 4 to roll a 9, 3 to roll a 10, 2 to roll an 11, and 1 way to roll a 12. We are asked for P(5), so 4/36 = 1/9. Q2: What is the probability of rolling an 11 with a standard pair of dice? 3. There are 7 letters. If they were all different, we could choose 7 to to first, 6 second, 5 thirds … etc., so 7! = 5,040. However, there are two A’s and two R’s in ARRANGE. Number them to see that A1R1R2A2NGE is the same as A2R1R2A1NGE and A1R2R1A2NGE and A2R2R1A1NGE because there are (2!) ways to arrange the A’s and (2!) ways to arrange the R’s. We must divide by (2!)(2!) to get 1,260 arrangements.