help!

 

Triangle DEF is an equilateral triangle with a side length of 3.     

A point P is chosen at random within triangle DEF.     

What is the probability that the length DP is at most 1?      

 

Draw an equilateral triangle DEF, side 3.     

Draw a circle, center at D, 1 inch radius.     

 

DP will be < 1 if it falls in or on the sector of the circle     

that's inside the triangle.     

 

Area of entire circle  =  (3.1416) • 1²  =  3.1416     

Area of sector inside triangle  =  (60^o / 360^o) • 3.1416  =  0.5236     

 

Area of triangle (per formula)  =  [ sqrt(3) / 4 ] • 3²  =  3.8971     

 

Probability  =  0.5236 / 3.8971  =  0.1344  ——>  as a percent  =  13.44%     

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