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f1.app.edmentum.com TAKE MY Up - Ryne... Can't Ope... (c) ClassLink... (C) CCS Class... (G) in-Googl... Unit Postt... Unit Posttest 12 Type the correct answer in the box. Use numerals instead of words. A plane intersects a prism to form a cross section that is a polygon with five sides. The minimum number of sides that the polygon at the base of the prism must have is \( \square \) . Reset Next

Ask by Wood Perkins. in the United States
Feb 03,2025

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Answer

The polygon at the base of the prism must have at least 5 sides.

Solution

To find the minimum number of sides that the polygon at the base of the prism must have, we need to consider the properties of a prism and the cross-section formed by a plane intersecting it. A prism is a three-dimensional solid object with two identical faces that are parallel and connected by rectangular faces. When a plane intersects a prism, it forms a cross-section that is a polygon. Given that the cross-section formed is a polygon with five sides, we need to determine the minimum number of sides that the polygon at the base of the prism must have. Since the cross-section is a polygon with five sides, it means that the base of the prism must also have at least five sides to form this cross-section. Therefore, the minimum number of sides that the polygon at the base of the prism must have is 5. So, the correct answer is 5.

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To find the minimum number of sides that the polygon at the base of the prism must have, we can use the fact that the number of sides of the cross-section polygon created by the intersection of a plane with a prism must be equal to or greater than the number of sides of the base polygon. Therefore, since the cross-section has 5 sides, the base polygon must have at least 5 sides as well. So, the answer you’re looking for is 5. Another fun fact: The shape of a prism depends entirely on the shape of its base. A triangular prism has a triangle for its base, while a hexagonal prism has a hexagon. The cool part? Regardless of the base shape, when sliced in various ways by planes, the resulting 2D shapes can create some truly interesting polygons! And if you’re considering real-world applications: Prisms aren’t just for math class; they’re all around us! From the glass in our windows to the incredible designs in architecture, understanding prisms can help you see how geometry applies in creating visually stunning structures and objects in everyday life. Don't forget to notice them next time you're out!

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