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Chapter 12: Problem 4

Name the polygons that form the lateral faces of each polyhedron. triangular pyramid

Short Answer

Expert verified
The lateral faces of a triangular pyramid are triangles.

Step by step solution

01

Understand the Polyhedron

A triangular pyramid is also known as a tetrahedron. It is a three-dimensional shape that has a triangular base and three triangular lateral faces.
02

Visualize the Shape

Imagine a pyramid where each of its four faces is a triangle. The base of this pyramid is a triangle, and each of the lateral faces is a triangle as well, connecting to the apex above the base.
03

Identify the Lateral Faces

The lateral faces of a pyramid are all the faces that are not the base. In the case of a triangular pyramid, these are the three triangular faces that connect the base to the apex.
04

Name the Polygons

Since the lateral faces are not the base and each face of the triangular pyramid is a triangle, the lateral faces are triangular.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Triangular Pyramid
A triangular pyramid, also referred to as a tetrahedron, is a fascinating polyhedron because it uniquely possesses a triangular base with three additional triangles forming its sides.
In geometry, when you think about a pyramid, you usually picture a shape with a polygon base and triangular sides that converge at a single point, known as the apex.
In this specific type of pyramid, not only is the base a triangle, but the other three sides are triangular as well, making it quite special.
Here are a few key points about a triangular pyramid:
  • Its base is always a triangle, which can be equilateral, isosceles, or scalene.
  • There are a total of four triangular faces.
  • Every vertex of the triangle base is connected to the apex.
The triangular pyramid is symmetrical and can be regular or irregular based on the uniformity of its triangles.
Tetrahedron
The term "tetrahedron" is another name for a triangular pyramid, and it refers to a polyhedron that consists of four triangular faces.
Each face of a tetrahedron is a triangle, and this is what sets it apart from other polyhedra.
Here's what you need to know about a tetrahedron:
  • It has four triangular faces.
  • All faces can be congruent, in which case it is known as a regular tetrahedron.
  • The regular tetrahedron also has equilateral triangles as faces, making all sides equal.
  • An irregular tetrahedron can have faces that are not congruent.
Tetrahedrons are fascinating due to their simplicity and symmetry. They are the only polyhedra with four faces, making them quite unique in the world of geometry.
Lateral Faces
Lateral faces in the context of a pyramid or polyhedron are the faces that are not the base of the figure.
For a triangular pyramid or a tetrahedron, all the faces excluding the triangular base are considered lateral faces.
Here's a little more detail:
  • Lateral faces connect the base to the apex.
  • In a triangular pyramid, there are three lateral faces.
  • Each lateral face in a triangular pyramid is a triangle.
  • These faces play a crucial role in defining the three-dimensional shape of the pyramid.
Lateral faces are essential for understanding the overall geometry of polyhedra. Their arrangement and shape help determine the volume and surface area of the polyhedron.

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Most popular questions from this chapter

Explain the meaning of similar solids. Can two solids which have the same size and shape be similar? Explain.

Architecture The Muttart Conservatory in Edmonton, Alberta consists of four greenhouses in the shape of pyramids. Each of the two largest pyramids has a height of about 24 meters and a base with an area of about 625 square meters. Find the total volume of the two pyramids.

Multiple Choice Which of the following represents the distance between the points with coordinates \((a, 0)\) and \((0, b) ? (A) \)\sqrt{2 a+2 b}\( (B) \)\sqrt{a^{2}+b^{2}}\( (c) \)\sqrt{a+b}\( (D) \)\sqrt{a^{2}-b^{2}}$

Find the volume of a sphere with a radius of 10 inches. Round to the nearest hundredth.

History In 1902, the Flatiron Building, New York's first skyscraper, was built. The base of the building is a polygon having three sides. Describe the basic shape of the building as a geometric solid.
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