Show that if there is an Archimedean solid that has faces that are regular pentagons and equilateral triangles, and where four faces meet at each vertex, then there must be eight more triangles than pentagons.

Q: 66. LA = TA = V = 6 ft I I 16 ft

A: For a cylinder whose radius is r and height is h  Lateral surface area ( LA ) = 2πrh Total surface…

Q: Find the dimensions of the argest rectangle that can be placed inside a triangle whose base lemgth…

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Q: A rhombus can be divided by its diagonals into four 3-4-5 right triangles. What is its area?

A: To find the area of rhombus

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 soccer ball has 32 faces, each of which is a regular pentagon or hexagon. Because of the angles…

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Q: The basic unit for measuring area does not have to be a square. Measure the area of the concave…

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Q: Draw a polyhedron from a different angle that is congruent to the one below.

A: Congruency means that the figure is similar to the other one and can complete overlap themselves.

Q: How large of an equilateral triangle can you fit inside a 2-by-2 square? Two of the three vertices…

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Q: If the area of a rhombus is 112 cm? and one of its diagonal is 14 cm find its othe

A: topic - area of rhombus from its diagonals

Q: Let three vertices of a triangle be ?(4, 0, 1), ?(1, 5, 2), and ?(−4, 1, −3). What is the area of…

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Q: Every polyhedron can be unfolded into a two-dimensional flat surface. O True O False

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Q: D с B

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Q: The cover of a soccerball consists of in- terlocking regular pentagons and regular hexagons, as…

A: The Pentagon has 5 sides and 5 vertex angles. While hexagon has 6 sides and six vertex angles The…

Q: Sketch a 4-dimensional triangle (also known as a simplex), unfolded into three dimensions.  How many…

A: A 4-D triangle is made by taking 5 3-D triangles and connecting them together .

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: A prism contains two types of faces: bases and lateral faces. O True O False

A:

Q: If the three vertices of a triangle have coordinates(0,0), (0,3), and (5,0)how many square units are…

A: Given data:   The given first coordinate of the triangle is: A=(x1,y1)=(0,0). The given second…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.