Can you send me full source code in python? So that I can run on colab?$[10$ marks$]$ Use Monte Carlo method to estimate the area of the shaded region. Also

make a scatter plot of your sample points as we did in our lecture. Color the rectangle

green, half circle red, both triangle blue.

I did it but there is a problem on this code for the triangle part please make correction and give me full code

import numpy as np

import matplotlib.pyplot as plt

def estimate$\_$area$($num$\_$samples$)$:

points$\_$inside$\_$rectangle $=0$

points$\_$inside$\_$half$\_$circle $=0$

points$\_$inside$\_$triangle$1=0$

points$\_$total $=$ num$\_$samples

for $\_$ in range$($num$\_$samples$)$:

x $=$ np$.$random.uniform$(0,10)$

y $=$ np$.$random.uniform$(0,8)$

# Check if point is inside the green rectangle

if $($x $>=2)$ and $($x and $($y $>=0)$ and $($y :

points$\_$inside$\_$rectangle $+=1$

# Check if point is inside the upper semi$-$circle

elif $(($x $-4)**2+($y and $($y $>=4)$:

points$\_$inside$\_$half$\_$circle $+=1$

# Check if point is inside the triangle $(6,0),(8,2),(6,4)$

elif $($x $>=6)$ and $($x and $($y $>=0)$ and $($y and $($y x $-12)$ and $($y x $+20)$:

points$\_$inside$\_$triangle$1+=1$

# Estimate area

total$\_$area $=10*8$

shaded$\_$area $=$ total$\_$area $*(($points$\_$inside$\_$rectangle $+$ points$\_$inside$\_$half$\_$circle $+$ points$\_$inside$\_$triangle$1)/$ points$\_$total$)$

return shaded$\_$area

def plot$\_$points$($num$\_$samples$)$:

x$\_$rectangle$\_$inside $=[]$

y$\_$rectangle$\_$inside $=[]$

x$\_$half$\_$circle$\_$inside $=[]$

y$\_$half$\_$circle$\_$inside $=[]$

x$\_$triangle$\_$inside $=[]$

y$\_$triangle$\_$inside $=[]$

for $\_$ in range$($num$\_$samples$)$:

x $=$ np$.$random.uniform$(0,10)$

y $=$ np$.$random.uniform$(0,8)$

if $($x $>=2)$ and $($x and $($y $>=0)$ and $($y :

x$\_$rectangle$\_$inside.append$($x$)$

y$\_$rectangle$\_$inside.append$($y$)$

elif $(($x $-4)**2+($y and $($y $>=4)$:

x$\_$half$\_$circle$\_$inside.append$($x$)$

y$\_$half$\_$circle$\_$inside.append$($y$)$

elif $($x $>=6)$ and $($x and $($y $>=0)$ and $($y and $($y x $-12)$ and $($y x $+20)$:

x$\_$triangle$\_$inside.append$($x$)$

y$\_$triangle$\_$inside.append$($y$)$

plt$.$figure$($figsize$=(8,6))$

plt$.$scatter$($x$\_$rectangle$\_$inside, y$\_$rectangle$\_$inside, color$=$'green', label$=$'Rectangle Inside'$)$

plt$.$scatter$($x$\_$half$\_$circle$\_$inside, y$\_$half$\_$circle$\_$inside, color$=$'red', label$=$'Half Circle Inside'$)$

plt$.$scatter$($x$\_$triangle$\_$inside, y$\_$triangle$\_$inside, color$=$'blue', label$=$'Triangle Inside'$)$

# Plot rectangle

rect$\_$points $=$ np$.$array$([[2,0],[6,0],[6,4],[2,4],[2,0]])$

plt$.$plot$($rect$\_$points$[$:$,0],$ rect$\_$points$[$:$,1],$ color$=$'green', label$=$'Rectangle'$)$

# Plot upper semi$-$circle

theta $=$ np$.$linspace$(0,$ np$.$pi$,100)$

circle$\_$x $=4+2*$ np$.$cos$($theta$)$

circle$\_$y $=4+2*$ np$.$sin$($theta$)$

plt$.$plot$($circle$\_$x$,$ circle$\_$y$,$ color$=$'red', label$=$'Upper Semi$-$circle'$)$

# Plot triangle $(6,0),(8,2),(6,4)$

triangle$\_$points $=$ np$.$array$([[6,0],[8,2],[6,4],[6,0]])$

plt$.$plot$($triangle$\_$points$[$:$,0],$ triangle$\_$points$[$:$,1],$ color$=$'blue', label$=$'Triangle'$)$

plt$.$xlim$(0,10)$

plt$.$ylim$(0,8)$

plt$.$xlabel$(\text{'}$X$\text{'})$

plt$.$ylabel$(\text{'}$Y$\text{'})$

plt$.$title$(\text{'}$Monte Carlo Method $-$ Sample Points'$)$

plt$.$legend$()$

plt$.$show$()$

# Number of samples

num$\_$samples $=10000$

# Estimate area

estimated$\_$area $=$ estimate$\_$area$($num$\_$samples$)$

print$("$Estimated area of shaded region:", estimated$\_$area$)$

# Plot sample points

plot$\_$points$($num$\_$samples$)$