Answer:
41.24 cm²
Step-by-step explanation:
Here is the complete question: A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?
Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]
Radius of circle is 4 cm.
We can find the area of shaded region by subtracting area of rectangle from area of circle.
First, lets find the area of rectangle
Formula; Area of rectangle= [tex]length\times width[/tex]
Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]
∴ Area of rectangle= 9 cm²
Now, finding the area of circle.
Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)
Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]
∴ Area of circle= 50.24 cm²
Next solving to find area of shaded region.
Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]
Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]
∴ Area of shaded region= 41.24 cm²
