Explain how many vertices, edges, and faces the polyhedron have. Does it verify Euler's Formula?

Q: Is there a regular polygon with 7 diagonals? Yes No If so, how many sides does it have? (If such a…

A: We know that  Diagonals of polygon=n(n-3)/2 .... equa 1 Here, n is number of side of polygogons…

Q: A polyhedron has 6 faces and 7 vertices. How many edges does it have?

A: Polyhedron is a three dimensional solid structure formed by joining polygons. Let F be the number of…

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

A: there are given faces, vertices and edges. we have to find which polyhedron exists. we know the…

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

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Q: How many triangles can you make using 6 non collinear points on a plane?

A: we have to solve above question

Q: For the regular pentagonal prism shown below, find the total number of a) edges. b) faces.

A: Given: A regular pentagonal prism: To determine: Number of edges & number of faces in a regular…

Q: An artist joined three square regions at their vertices to create the figure shown in the diagram.…

A: Given

Q: A polyhedron has 6 edges and 4 vertices. How many faces does it have ?

A: By Euler formula  F+V = E +2  F = Number of Faces  V = Number of vertices E= Number of Edges

Q: Which figure represents the net of a triangular prism?

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Q: Construct a polyhedron that has 9 edges.

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Q: Can you make a pyramid in which the triangular faces are not all congruent?

A: We need to draw a pyramid whose triangular faces are not all congruent.

Q: A polyhedron has 9 faces and 21 edges. How many vertices does it have ?

A: A polyhedron has 9 faces and 21 edges. F=9 and E=21. The objective is to find the number of vertices…

Q: For the polyhedron, use Euler's Formula to find the missing number.

A: Euler's formula states that The number of vertices V, faces F, and edges E in a convex 3-dimensional…

Q: Philolaus called the cube a “geometric harmony," because of the num- ber of its faces, vertices, and…

A: Given: History of math-Philolaus called the cube a geometric harmony" because of the number of it's…

Q: A polyhedron has 12 faces and 30 edges. How many vertices does it have ?

A: Given,            A polyhedron has 12 faces and 30 edges.

Q: A polyhedron (not regular) has 14 vertices and 21 edges. How many faces must it have?

A: Given that a polyhedron has 14 vertices and 21 edges. We need to find how many faces does the…

Q: How many triangles are formed by drawing all the diagonals from a single vertex?

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Q: Write a formula that connects the number of sides of the base, S, with the number of edges, E.…

A:

Q: does a 12-sided co

A: Here we have to find the number of diagonals of a 12-sided convex polygon.

Q: Can a polyhedron have 3 faces, 4 vertices, and 5 edges? Explain.

A: Euler's formula for a polyhedron  For any polyhedron F+V-E=2 Where  F = number of faces  V = number…

Q: Given a cyclic quadrilateral whose sides are 4 cm, 5 cm, 8 cm, and 11 cm. Its area is

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Q: How many lines of symmetry does a regular hexagon have?

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Q: For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then…

A: Given: regular hexahedron To find :  Number of faces,…

Q: Starting with a cube with edges of length 2, the corners are cut-off to form a cuboctahe-dron. To do…

A: Given: A polyhedron having 8 triangular faces and 6 square faces are known as a cuboctahedron. A…

Q: Consider the triangular prism shown. (a) How many vertices does it have? (b) How many edges (lateral…

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Q: A polyhedron (not regular) has 10 vertices and 6 faces. How many edges does it have? edges

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Q: For a regular tetrahedron, find the number of faces, vertices, and edges in the polyhedron. Then…

A: Given- A regular tetrahedron. To find- The number of faces , vertices and edges and then verify the…

Q: Use Euler's Theorem to find the value of n. 4) What is the number of faces? If the solid has 12…

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Q: Every N-final prism has n lateral faces. Is the statement true or false.

A: For an n gonal prism, if it is toroidal prism then it will have: 3n Edges 2n Vertices and  2+n faces…

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

A: We solve the question by using Euler's formula F + V - E=  2, where F is the number of faces, V the…

Q: ) What attributes do all cylinders and cones have that not all three-dimensional figures have?…

A: Given that:A) All cylinders and cones                     B) All cylinders and all prisms

Q: If 2 of the vertices of an inscribed quadrilateral are on the diameter, will the inscribed always be…

A: If all the vertices of an inscribed quadrilateral are on the diameter, then the diagonals of the…

Q: For the polyhedron, use Euler's Formula to find the missing number. faces: edges: 13 vertices: 9 The…

A: According to the problem,we have

Q: For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then…

A:

Q: how many vertices does a 28-sided polygon have

A: Solution: The objective is to find how many vertices does a 28-sided polygon have.

Q: A polyhedron (not regular) has 11 vertices and 9 faces. How many edges does it have?

A: We have to find edges

Q: How many edges does a tetrahedron have ?

A:

Q: If a polygon of n sides has 1/2n(n - 3) diagonals, how many sides will a polygon with 65 diagonals…

A: The number of diagonals of polygon with n sides is given by nn-32.   Consider that a polygon has 65…

Q: A polyhedron (not regular) has 10 vertices and 7 faces. How many edges does it have?

A: Given that polyhedron has 10 vertices and 7 faces. We need to find the number of edges in the…

Q: Find the number of sides of a convex polygon if the measures of its interior angles have a sum of…

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Q: How many vertices does a hexahedron have ?

A: A hexahedron, as the name suggests, is a six faced polyhedron. A cube is an example of a hexahedron

Q: For the polyhedron, use Euler's Formula to find the missing number. faces: 8 edges: vertices: 6

A: Euler's formula is: F+V=E+2

Q: How many side does a tetrahedron have ? How many number of edges which meet at a vertex does a…

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Q: What polygon is formed by the intersection of plane N and the octagonal prism shown?

A: Here the intersection is formed by the plane N and octagonal prism. Polygon formed is just an…

Q: Define a polyhedron with 20 faces ?

A: We have to define a polyhedron with 20 faces.

Q: Consider this Platonic Solid, the cube:How many faces?  edges?  vertices?

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Q: 14. 15. 13. 14. Mathematics in the Modern World 15.

A: Given : Solid structure is given

Q: A solid is an octagonal prism. a) How many vertices does it have? b) How many lateral edges does it…

A: Given:A  solid is  an octagonal prism   Octagonal prism has10 faces24 edges16 vertices

Q: An apothem of a regular polygon is perpendicular to one of its sides. true or false?

A: To find- An apothem of a regular polygon is perpendicular to one of its sides.

Q: Find the number of vertices, edges, and faces of the given polyhedron

A: Vertices: The  corners Faces: The sides of the shape Edges: Where the faces meet