ttop0816
  • ttop0816
Find the volume for the regular pyramid. https://media.glynlyon.com/g_geo_2012/8/groupi7 7.gif V =
Mathematics
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schrodinger
  • schrodinger
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anonymous
  • anonymous
The formula for finding the volume of the pyramid is V = 1/3 * area of base * height. To find the area of the base in this case, use the equilateral triangle formula: http://www.mathopenref.com/triangleequilateralarea.html The area of the base will turn out to be 6.93.
anonymous
  • anonymous
Next, to find the height, we use the 30-60-90 triangle theorem. Since all triangles' angles are 60 degrees, we can draw an altitude down like this to make such a triangle: |dw:1377874732434:dw|
anonymous
  • anonymous
The theorem states that all sides opposite to the angles 30-60-90 will have a ratio of x-x√3-2x respectively. And since 4 is opposite to 90 degrees, it has a ratio of 2x. 4 = 2x . What is x? x = 2. So the angle opposite to the 30 degrees triangle is 2 while the angle opposite to the 60 degrees angle is 2√3.|dw:1377875025749:dw|

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anonymous
  • anonymous
2√3 is our height. Now plug all of these into the volume formula. V = 1/3 * 6.93 * 2√3 and what do you get?

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