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Volume of Triangular Pyramid: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Volume of Triangular PyramidVolume of Triangular Pyramid: Definition and ExamplesTable of ContentsVolume of a Triangular Pyramid Definition of Volume of a Triangular Pyramid

A triangular pyramid is a three-dimensional shape with flat triangular faces, straight edges, and sharp corners or vertices. It consists of three triangular faces and a triangular base, totaling four faces, six edges, and four vertices. If all four faces are equilateral triangles, it's called a regular triangular pyramid (also known as a tetrahedron).

The volume of a triangular pyramid measures the space occupied within its boundaries in three-dimensional space. It can be calculated using the formula V=13×B×hV = \frac{1}{3} \times B \times hV=31​×B×h cubic units, where VVV is the volume, BBB is the base area, and hhh is the height of the pyramid. For a regular triangular pyramid with side length aaa, the volume can be found using V=a362V = \frac{a^3}{6\sqrt{2}}V=62​a3​ cubic units.

Examples of Volume of a Triangular Pyramid Example 1: Finding the Volume with Given Base Area and Height Problem:

What is the volume of a triangular pyramid if its base area is 19 sq. inches and its height is 1.5 inches?

Step-by-step solution:

Step 1, Write down what we know. We have base area B=19B = 19B=19 sq. inches and height of the pyramid h=1.5h = 1.5h=1.5 inches.

Step 2, Use the volume formula. We know that Volume =13×B×h= \frac{1}{3} \times B \times h=31​×B×h.

Step 3, Put the values into the formula. Volume=13×19×1.5\text{Volume} = \frac{1}{3} \times 19 \times 1.5Volume=31​×19×1.5

Step 4, Calculate the result. Volume=19×0.5=9.5\text{Volume} = 19 \times 0.5 = 9.5Volume=19×0.5=9.5 cubic inches

So the volume of the triangular pyramid is 9.5 cubic inches.

Example 2: Finding the Height of a Triangular Pyramid Problem:

Find the height of a triangular pyramid with a base area of 175 sq. units and a volume of 1,050 cubic units.

Step-by-step solution:

Step 1, List what we know. Base area B=175B = 175B=175 sq. units and volume V=1,050V = 1,050V=1,050 cubic units.

Step 2, Use the volume formula and substitute the values.

Volume of a triangular pyramid =13×B×h= \frac{1}{3} \times B \times h=31​×B×h

1,050=13×175×h1,050 = \frac{1}{3} \times 175 \times h1,050=31​×175×h

Step 3, Rearrange the formula to find the height. h=3×1,050175h = \frac{3 \times 1,050}{175}h=1753×1,050​

Step 4, Calculate the height. h=18h = 18h=18 units

So, the height of the pyramid is 18 units.

Example 3: Finding the Volume of a Regular Triangular Pyramid Problem:

What is the volume of a regular triangular pyramid with a side of length 929\sqrt{2}92​ units?

Step-by-step solution:

Step 1, Identify what we know. The side length of a regular triangular pyramid is a=92a = 9\sqrt{2}a=92​ units.

Step 2, Recall the formula for the volume of a regular triangular pyramid. V=a362V = \frac{a^3}{6\sqrt{2}}V=62​a3​

Step 3, Substitute the value of a=92a = 9\sqrt{2}a=92​ into the formula. V=(92)362V = \frac{(9\sqrt{2})^3}{6\sqrt{2}}V=62​(92​)3​

Step 4, Simplify the expression. V=92×92×9262V = \frac{9\sqrt{2} \times 9\sqrt{2} \times 9\sqrt{2}}{6\sqrt{2}}V=62​92​×92​×92​​

Step 5, Calculate the result. V=243V = 243V=243 cubic units

So, the volume of the regular triangular pyramid is 243 cubic units.

Comments(3)BBrandManagerUmaNovember 4, 2025This glossary page is a lifesaver! The formula and examples made it easy for my students to grasp the volume of a triangular pyramid. Thanks!

GGuardXenaNovember 4, 2025This glossary page on the volume of a triangular pyramid is great! It helped my students grasp the concept easily. Thanks for the clear examples!

NNatureLover85September 17, 2025This explanation made teaching the volume of a triangular pyramid so much easier for my kids! The step-by-step examples really helped them understand the formula. Great resource, thanks!

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