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Hey! Use the figure above to find the probability that a point chosen randomly inside the rectangle is in the specified shape.

So what's the probability that the point will be in the:
 

1. The square

2. The equilateral triangle

3. The parts of the circle (that's not included in the square)

4. The parts of the rectangle that's not included in the triangle, circle, or square.

 

Thank you!!

 Apr 17, 2021
 #1
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1.   Half  the length  of  the  base of the rectangle  can  be  found  as

 

24/sqrt 3

 

So....the  whole  base length = 48/sqrt 3  =  16sqrt 3 

 

So.......Area  of  rectangle  =  24 * 16sqrt 3  =   384sqrt (3)

 

Side  of  the square=  8sqrt (2) ....area of the square = S^2  =  (8sqrt (2))^2  = 128

 

P(  that  a point falls into the  square ) =  128 /( 384 sqrt (3) ) ≈  .192  = 19.2%

 

 

2.  Area of eqquilateral triangle =  (1/2) (16sqrt (3) )^2  * sqrt (3) / 2  =  192sqrt 93)

 

P(  that  a point falls into  the  equilateral triangle )  =  192sqrt (3)  / 384sqrt (3)  =  1/2  = 50%

 

3.  Area of circle  not including inside the  square=  pi *8^2  - 128

 

P  that a point  fals into  this  area =  [ pi *8^2  - 128 ]  / ( 384sqrt (3) )  ≈ .1098 = 10.98%

 

4.  Probabilty  that a point falls  into 4. the parts of the rectangle that's not included in the triangle, circle, or square  

 

The  area of the  equilateral trinagle   takes up 50%  of the area of  the  rectangle....so....the probability of falling outside the  triangle, circle or square   is also 50%

 

cool cool cool

 Apr 17, 2021
 #2
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Thank you so much!

Guest Apr 17, 2021

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