What is a Triangular-Based Pyramid?

What is a Triangle-Based Pyramid?

A triangle-based pyramid has four triangular sides.The base of a triangle pyramid can be any type of triangle, but is usually an equilateral triangle. This means that all sides and faces are the same. When rotated or placed in any position, it will look the same.

A triangle-based pyramid is unique in comparison to other pyramids, as it only consists of one kind of 2D shape, a triangle.

Properties of a Triangle Based Pyramid

Faces:

Triangle-based pyramids are formed exclusively of triangles. You can easily recognise a triangle-based pyramid by looking at the triangular sides that slant upwards from the triangular base.

A triangle-based pyramid consists of 4 triangles, because of this, a triangle-based pyramid is also known as a tetrahedron. If all faces are equilateral triangles, the pyramid is termed a regular tetrahedron. If the triangles have edges of different lengths, the pyramid is an irregular tetrahedron.

Edges:

Triangle-based pyramids have 6 edges. They have 3 along the base, and 3 extending up from the base. If the 6 edges of the triangle based pyramid are equal in length, the triangles are equilateral, and the triangle based pyramid is a regular tetrahedron.

Vertices:

All triangle-based pyramids have 4 vertices, regardless of whether they are regular tetrahedrons, or irregular tetrahedrons.

Apex:

The top of the pyramid is called the apex. This is where the edges meet in the middle.

Net:

The net of a triangle-based pyramid is made up of 4 triangles when laid flat. The base of the pyramid is a triangle, and the lateral faces are also triangles.

An example of a net of a triangle based pyramid

Measuring a Triangle Based Pyramid

Surface Area

To work out the surface area of a triangle-based pyramid, you need to add together the area of the base plus the area of all of the sides.

For a regular tetrahedron, you need to find the length of the base, and the height of 1 of the triangles. Then, you multiply these measurements together and divide the answer by 2.

The number you have as the answer is the area of 1 of the triangles.Then, multiply this number by 4 to account for all faces on the pyramid.

For an irregular tetrahedron, you need to find the area of each triangle individually, then you need to add all areas together.

Volume

If you want to work out the volume of any triangle-based pyramid, you need to multiply the area of the triangle base by the height of the pyramid.

You measure the height from the midpoint of the base to the apex. Then you divide this number by 3 to get your answer.

Facts to Remember

Take a look at this list of useful facts below to help you remember more about triangle-based pyramids:

• A triangle-based pyramid with equal edges and faces is called a regular tetrahedron.
• A triangle-based pyramid with unequal edges and faces is called an irregular tetrahedron
• A triangle-based pyramid has 6 edges
• A triangle-based pyramid has 4 faces
• The net of a triangle-based pyramid folds out to a large triangle made up of 4 smaller triangles.
• A triangle-based pyramid has 4 vertices.

Useful Resources

Take a look at some fantastic resources available you might like to use to aid your teaching on 3D shapes.

• Pyramid Shape Worksheet – This is a great introduction to square-based and triangle-based pyramids on a simple worksheet.
• Pyramid 3D Shape Paper Model – This handy paper model can be used as a way to help children understand how 2D nets can represent 3D pyramids.
• Real Life Object 3D Shapes Pack – You can use this pack to show children the connection between 3D shapes and the world around us.
• 2D and 3D Shape Riddle Cards Game – To help children learn the properties of different 2D and 3D shapes, use these riddle cards to challenge their knowledge.
• Name 3D Shapes Worksheet – Easy to print in black and white for a helpful supplement in maths lessons.
• 3D Shapes and their Nets PowerPoint – Use this PowerPoint to kick off a lesson about 3D shapes and their nets before getting stuck in with some of our worksheets.