A triangle pyramid is a geometric solid through a triangular base, and all three lateralfaces are additionally triangles v a common vertex. The tetrahedron is a triangle pyramid v equilateral triangle on every face. 4 triangles form a triangle pyramid.Triangular pyramids room regular, irregular, and also right-angled.

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**A three-dimensional shape with all its four faces as triangle is well-known as a triangle pyramid.**

1. | What isTriangular Pyramid? |

2. | Types of triangular Pyramid |

3. | Propertiesof a triangular Pyramid |

4. | Triangular Pyramid Formulas |

5. | Solved examples onTriangular Pyramid |

6. | Practice questions on triangular Pyramid |

7. | FAQs on triangular Pyramid |

## What isTriangular Pyramid?

A triangle pyramid is a 3D shape, all of the deals with of which space made in the type of triangles. A triangular pyramid is a pyramid with a triangle base and bounded by 4 triangular deals with where 3 faces meet in ~ one vertex. Thebase is a right-angle triangle in a best triangular pyramid, when other deals with areisosceles triangles.

### Triangular Pyramid Nets

The net patternis different for different varieties of solids.Nets room usefultofind the surface ar area of solids. A triangular pyramid netis a pattern that forms when its surface ar is to adjust flat, showing each triangular facet of a shape. The triangular pyramid netconsists of 4 triangles. The base of the pyramid is a triangle; the side faces are likewise triangles.

Let us do a small activity. Take it a sheet of paper.You can observe 2 differentnets the a triangle pyramidshown below.Copy this ~ above thesheet of paper. Cut it along the edge and also fold it as displayed in the picture below. The folded file forms atriangular pyramid.

## Types of triangle Pyramid

Like any other geometrical figure, triangle pyramids can also be classified right into regular and irregular pyramids. The different species of triangle pyramids are described below:

### Regular triangle Pyramid

A consistent triangular pyramidhas it is provided triangles together its faces. Since it is make of equilateral triangles, every itsinternal angles will certainly measure 60°.

### Irregular triangle Pyramid

An irregular triangular pyramidalso has actually triangular faces, however they are not equilateral. The internalangles in each plane include up come 180° as theyare triangular. Uneven a triangular pyramidis specificallymentioned asirregular,all triangle pyramidsare assumed to beregular triangular pyramids.

### Right triangle Pyramid

The best triangular pyramid (a three-dimensional figure) has a right-angle triangle base and the apex aligned above the center of the base. That has1 base, 6 edges, 3 faces, and also 4 vertices.

**Important Notes**

## Propertiesof a triangular Pyramid

Properties that a triangle pyramid help us to identify a pyramid native a given set of figures quickly and easily. The various Propertiesof a triangular Pyramid are:

It has actually 4 faces, 6 edges, and 4 vertices.At each of its vertex, 3 edges meet.A triangle pyramidhas no parallel faces.Triangular Pyramidsare discovered asregular, irregular, and right-angled.## Triangular Pyramid Formulas

There are assorted formulas to calculation the volume, surface ar area, and perimeter of triangular pyramids. Those formulae are given below:

To find the volume that a pyramidwith a triangle base, main point the area of the triangular basic by the height of the pyramid (measured from basic to top). Then divide that product through three.

**Triangular PyramidVolume = 1/3 × base Area × Height**

The slant elevation of a triangle pyramid is the distance from its triangular base follow me the center of the confront to the apex.To identify the surface ar area that a pyramid through a triangle base, add the area that the base and the area of all sides.

**Triangular Pyramid surface Area(Total) = basic Area + 1/2(Perimeter × Slant Height)**

Now consider a continuous triangular pyramidmade the equilateral triangle of next a*.*

Regular triangle Pyramid Volume = a3/6√2

Regular triangle PyramidSurface Area(Total) = √3a2

### Right triangle Pyramid Formulas

Surface AreaofaRight triangle Pyramid ((A_s)) = 1/2 ((h_b) × a) + 3/2 (a × (h_s))

The volume that a right Triangular Pyramid (V) = 1/6× (h_b) × a × h = 1/3× (A_b) × h

Where (A_s) = surface Area,(A_b) = basic Area, V= Volume, a= Edge, h= Height,(h_b) = height Base, and(h_s) = elevation Side.

**Challenging Questions:**

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**Example 1:**** Sid gained to understand that two triangular pyramids to be congruent.He startedobserving themfor their congruency. If he inserted the basic of both the triangle in a position to view if theyoverlap, the 2 congruent triangular pyramidsstuck together along its basic andformed a triangle bipyramid. How numerous faces, edges, and vertices go this bipyramid have?**

**Solution:** If we openup theabove image to check out the network of the triangle bipyramid,we have the right to observe this:

There are6 triangle faces, 9 edges, and also 5 vertices. ∴ triangular bipyramid has actually 6 triangular faces, 9 edges, and also 5 vertices.

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**Example 2: find the volume that a constant triangular pyramidwith a side size measuring5 units. (Round turn off the answer to 2 decimal places)**

**Solution: **We understand that for a triangular pyramidwhose next is a volume is:a3/6√2. Substituting a = 5, we get

Volume = 53/6√2

= 125/8.485

≈14.73

∴The volume the thetriangular pyramid is 14.73 units3

**Example 3:**** every edge that a consistent triangular pyramidis of length 6 units. Find its complete surface area.**

**Solution:** The complete surface area the a consistent triangular pyramidof side ais:√3a2. Substituting a= 6, we get,

TSA =√3 × 62= √3 × 6 × 6

= 62.35

∴ full Surface Area = 62.35 units2

**Example 4****: While solving questions about the triangle pyramid,Syna gained stuck. Let's aid her out to reach the last answer. Here's the question:"The sum of the length of the edge of a constant triangular pyramidis 60 units. Find the surface ar area of one of its faces."**

**Solution: **We recognize that atriangular pyramidhas 6 edges. And it's provided to it is in a consistent triangular pyramid. Therefore, the size of every edge is:60/6 = 10units. The surface area of one confront of the triangle pyramid: