Answer: 54.88
Step-by-step explanation:
The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 10. The width of the rectangle is the diameter of the circle, 8. First, find the area of the rectangle:
AAA=length×width=10⋅8=80
To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=4. Use the value of r to solve for the area:
AAA=πr2=3.14⋅(42)=50.24
Now we can subtract half the area of the circle from the area of the rectangle:
Area of rectangle−Area of half circle=Area shaded region
80−50.242
A=54.88
So the area of the shaded region is 54.88.
