An equilateral triangle has sides that are 6 cm long. What is the probability that a...
An equilateral triangle has sides that are 6 cm long. What is the probability that a point chosen at random in the triangle is within 1 cm of a corner?
Homework Answers
P[ a point chosen at random in the triangle is within 1 cm of a corner ] = Area within 1 cm of a corner / Area of triangle
Area of equilateral triangle of side a = 
For a = 6
Area of triangle = 
Area of triangle = 
Area of triangle = 15.59
Area within 1 cm of a corner = 3*area of sector with angle 60 and radius 1 cm
Area within 1 cm of a corner = 
Area within 1 cm of a corner = 
Area within 1 cm of a corner = 3.14
P[ a point chosen at random in the triangle is within 1 cm of a corner ] = 3.14/15.59
P[ a point chosen at random in the triangle is within 1 cm of a corner ] = 0.2014
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