Circles Inscribed in Squares
You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length , the following formulas are used.
For a circle with radius , the following formulas are used.
Find the perimeter of the square.
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.
So, the side length of the square is cm.
The perimeter of a square with side length is given by .
Substitute for in .
The perimeter of the square is cm.
What is the area of a circle that is inscribed in a square of area square units?
When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is units and therefore the radius is units.
The area of a circle of radius units is .
Substitute in the formula.
Therefore, the area of the inscribe circle is about square units.