large pizza at Tony's pizza is a circle with a 14 inch diameter it's box is a rectangular prism that is 14 1/8 inches long 14 1/8 inches wide and 1 3/4 inches tall you have to create a new shape for the pizza but it has to have at least 5 sides and be cut into equal slices. Please show all of your work
Plzzz answer I rlly need this quickly
To create a new shape for the pizza with at least 5 sides and equal slices, we can start by considering different regular polygons.
1. Hexagon: A hexagon has 6 sides, which is more than the required 5 sides. Each slice will have an angle of 360 degrees / 6 = 60 degrees. To determine if this shape can fit within the given dimensions, we need to calculate the maximum length of one side of the hexagon.
Since the diameter of the pizza is 14 inches, the radius is half of the diameter, which is 14 inches / 2 = 7 inches. The hexagon can be circumscribed around the circle, meaning its corners will touch the circle's circumference.
The length of each side of the hexagon is equal to the radius of the circle, which is 7 inches. Therefore, the length of one side of the hexagon is within the given dimensions.
2. Octagon: An octagon has 8 sides. Similar to the hexagon, we need to calculate the maximum length of one side.
Using the same calculations as before, the length of each side of the octagon is equal to the radius of the circle, which is 7 inches. Thus, the length of one side of the octagon is also within the given dimensions.
3. Decagon: A decagon has 10 sides. Following the same calculations, the length of each side of the decagon is equal to the radius of the circle, which is 7 inches. Hence, the length of one side of the decagon is within the given dimensions.
4. Dodecagon: A dodecagon has 12 sides. By calculating the length of each side, we find that it is also equal to the radius, which is 7 inches. Therefore, the length of one side of the dodecagon fits within the given dimensions.
Based on these calculations, we can conclude that all the mentioned regular polygons (hexagon, octagon, decagon, and dodecagon) can fit within the given dimensions of the pizza box. In each case, the length of one side of the polygon is within 14 1/8 inches, which is the longest dimension of the box.
To cut the pizza into equal slices, we need to divide the total angle of the shape (360 degrees for all regular polygons) by the number of sides. For example, for the hexagon, each slice will have an angle of 360 degrees / 6 = 60 degrees.
I hope this explanation helps you create a new shape for the pizza!