The shaded area is approximately 75.48 square units, rounded to the nearest hundredth.
To find the area of the shaded region in the figure, we can follow these steps:
Area of the Rectangle:
The rectangle's area is given by multiplying its length and width.
In this case, the length is the diameter of the circle, which is 12 units, and the width is the height of the rectangle, which is 10 units.
Area of rectangle=length × width=12×10=120square units
Area of the Quarter Circle:
The radius of the circle is half of the diameter, so it is 12/2 =6 units.
The area of a quarter circle is one-fourth of the area of the full circle, where the area of a circle is given by πr^2 .
Area of quarter circle= 1/4 π(6^2 )= 1/4 ×36π=9πsquare units
Area of the Shaded Region:
Subtract the area of the quarter circle from the area of the rectangle.
Shaded area=Area of rectangle−Area of quarter circle=120−9πsquare units
Given that π≈3.14, we can approximate the value:
Shaded area ≈ 120−9×3.14≈75.48 square units
Shaded area≈120−9×3.14≈75.48square units
Therefore, the correct answer for the shaded area is approximately 75.48 square units, rounded to the nearest hundredth.