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!!
+128475 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%
