we are given
three shapes
first is rectangle
second is circle
third is triangle
we can find area of each shapes and then subtract them accordingly to find shaded area
Area of rectangle:
length=l=18
width=w=6
we know that
area = length*width
[tex] Area=18*6 [/tex]
[tex] Area=108 [/tex]
Area of semicircle:
we are given
radius =r=6/2=3
now, we can find area
[tex] Area=\frac{1}{2} \pi r^2 [/tex]
[tex] Area=\frac{1}{2} \pi 3^2 [/tex]
[tex] Area=\frac{9}{2} \pi [/tex]
Area of triangle:
base=b=9
height=h=6
now, we can find area
[tex] Area=\frac{1}{2} *b*h [/tex]
[tex] Area=\frac{1}{2} *9*6 [/tex]
[tex] Area=27 [/tex]
Area of shaded region:
Area = rectangle -triangle -2*semicircle
so, we get
[tex] Area=108-27-2*\frac{9}{2} \pi [/tex]
we get
[tex] Area=52.72567 [/tex]
so, option-B..........Answer
