Final answer:
For the largest circular rug that Susie can fit in her dining room, the diameter of the circle will be the shortest side of the rectangle. The radius would be half of that and the area is then calculated using the formula for the area of a circle, πr².
Step-by-step explanation:
In Mathematics, to find the area of the largest circle that can be fit into a rectangle, we will make use of the rectangle's width or length depending on which is the shortest. The largest possible circle that can fit inside a rectangle would be a circle that has a diameter equal to the rectangle's shortest side.
Let's say the width of Susie's dining room is 'w' units and the length is 'l' units. We know, the diameter of the circle = min(l, w). The radius of the circle would be half of the diameter. Hence, radius = min(l, w)/2.
Knowing that the formula to calculate the area of a circle is πr², where r is the radius of the circle and π is approximately 3.14, we substitute min(l, w)/2 into the formula. We have Area = π * (min(l, w)/2)². This will give us the area for the largest circular rug that can be placed in Susie's dining room.
Learn more about Area of Circle