Table of Contents
About Triangular Pyramid
Triangular Pyramid – Types, Parts, Properties, Formulas, and Example Problems: A triangular pyramid is a pyramid with a triangular base. It is the simplest type of pyramid.
Pyramid
Pyramid is a triangular, three-sided shape that is widest at the base and narrower at the top. It is named for its resemblance to the shape of a pyramid in Egypt. Pyramids have been used for a variety of purposes, including as tombs for pharaohs and their consorts, as well as for other members of the royal family.
Types of Pyramids
There are three types of pyramids: The square pyramid, the triangular pyramid, and the Egyptian pyramid.
- The square pyramid is a pyramid with a square base.
- The triangular pyramid is a pyramid with a triangular base.
- The Egyptian pyramid is a pyramid with a triangular base and a square top.
1.Triangular Pyramid
A triangular pyramid is a pyramid with a triangular base.
Parts of a Triangular Pyramid
There are six triangular faces on a triangular pyramid. There are four vertices and six edges.
Properties of Triangular Pyramid
- A triangular pyramid is a three-sided pyramid with a triangular base.
- The height of a triangular pyramid is the length of the perpendicular from the base to the apex.
- The surface area of a triangular pyramid is the sum of the areas of the three triangular faces.
- The volume of a triangular pyramid is one-third the volume of a prism with the same base and height.
Different Triangular Pyramid Types
There are three types of triangular pyramids: right, acute, and obtuse.
- A right triangular pyramid has a right angle as its base.
- An acute triangular pyramid has an angle less than 90 degrees at its base.
- An obtuse triangular pyramid has an angle greater than 90 degrees at its base.
Formulas of Triangular Pyramid
- The height of a triangular pyramid is one-third the length of the base.
- The surface area of a triangular pyramid is half the base times the height.
- The volume of a triangular pyramid is one-third the base times the height times the density.
Volume of a Triangular Pyramid
The volume of a triangular pyramid is given by the formula:
V = 1/3bh
Where b is the base length, and h is the height.
Surface Area of Triangular Pyramid
The surface area of a triangular pyramid is the sum of the areas of the three triangular faces and the base.
A = (base area) + (1/2) * (sum of the areas of the two triangular faces)
A = (1/2) * (bh) + (1/2) * (bh)
A = (bh)
Example Problems
1. Find the area of a triangle with base 10 and height 8.
The area of the triangle is 80.
Triangular Prism
A triangular prism is a three-sided prism with six faces, twelve edges, and eight vertices. The three sides are congruent isosceles triangles, and the angles between the sides are 60°.
Properties of a Triangular Prism
A triangular prism is a three-sided prism with a triangular base. The triangular prism has six faces (three sides and three bases), eight edges (four along each side), and six vertices (three at each corner). The triangular prism is also called a right triangular prism because the base is a right triangle.
How Many Edges Has a Triangular Prism?
A triangular prism has six faces, each of which is a triangle. That means it has six edges.
Activity-1: Construction of a Triangular Pyramid
- Step 1: Determine the height of the triangular pyramid.
- Step 2: Draw a triangle with the height as the base.
- Step 3: Draw a line from the top of the triangle to the base.
- Step 4: Draw a line from the bottom of the triangle to the base.
- Step 5: Connect the lines to form the triangular pyramid.
Activity-2: How to Draw a Triangular Pyramid
1. Draw a square and label the vertices A, B, C, and D.
2. Draw a line from each vertex to the opposite vertex.
3. Connect the lines to form a triangle.
4. Draw a line from the top vertex to the bottom vertex.
5. Connect the line to form a triangle.
6. Draw the outline of the pyramid.
7. Draw the lines to indicate the sides of the pyramid.
