Answer:
The area of the biggest possible square that fit into the circle is 18 cm²
Step-by-step explanation:
* Lets talk about the square inscribed in a circle
- The square is fit into the circle if its four vertices lie on the
circumference of the circle
- The diagonal of the square is the diameter of the circle
- The vertices of the square divide the circle into 4 equal arcs
* Look to the attached figure
- The square ABCD fit into the circle M
- A , B , C , D lie on the circumference of the circle M
- The four arcs AB , BC , CD , AD are equal in measure and length
- The diagonal of the square is DB
- The diameter of the circle M is DB
∵ The radius of the circle is 3 cm
∵ The diameter = twice the radius
∴ The diameter of the circle = 2 × 3 = 6 cm
∴ DB = 6 cm
- The rule of the area of the square = (diagonal)²/2
∵ The length of the diagonal is 6 cm
∴ The Area of the square = (6)²/2 = 36/2 = 18 cm²
* The area of the biggest possible square that fit into the circle is 18 cm²
