To find: The volume of the pyramid in terms of
Answer to Problem 29WE
The volume of the pyramid in terms of
Explanation of Solution
Given information:
The length of all the edges of a regular triangular pyramid is equal to
Calculation:
Consider the regular triangular pyramid:
The length of each base edge of pyramid is equal. So, the length of the side
The length of the side
Consider the triangle
So, the length of the side
Use the Pythagoras theorem in
So, the height
The formula for the volume of pyramid is the one third of the product of base area and height.
Simplify the area of equilateral triangle with side
Substitute
Therefore, the volume of the pyramid in terms of
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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