Answer:
The area of the square is 1.266 [tex]in^2[/tex] less than the circle.
Step-by-step explanation:
The area of a square is given by the formula
[tex]area=width\times height[/tex]
But since the width and height are by definition the same, the formula is usually written as
[tex]area=s^2[/tex]
where s is the length of one side.
Given the radius of a circle, the area inside it can be calculated using the form
[tex]area=\pi r^2[/tex]
where r is the radius of the circle and [tex]\pi[/tex] is Pi, approximately 3.142.
So, the area of a square with a side length of 7 inches is
[tex]area_{square}=7^2=49\:in^2[/tex]
the area of a circle with a radius of 4 inches is
[tex]area_{circle}=\pi 4^2=3.142\cdot 16=50.266 \:in^2[/tex]
Now, we take the difference in the areas.
[tex]area_{square}-area_{circle}=49-50.266=-1.266\:in^2[/tex]
Because the difference between the areas of the square and the circle is negative, the area of the square is 1.266 [tex]in^2[/tex] less than the circle.
