Find the volume for the regular pyramid

https://media.glynlyon.com/g_geo_2013/8/groupi77.gif

Question

Find the volume for the regular pyramid

https://media.glynlyon.com/g_geo_2013/8/groupi77.gif

mathstudent55 · Answer

Volume of a pyramid:

$V = \dfrac{1}{3}Bh$

where B = area of the base, and
h = height

anonymous · Answer

@mathstudent55 i know that the area of the base is 4 sqrt 2 but how do i find the height

mathstudent55 · Answer

This is the base of the pyramid.
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mathstudent55 · Answer

For the area of the base:
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mathstudent55 · Answer

Area of the base is $4\sqrt{3} $

mathstudent55 · Answer

Ok. Now we still need the height.

anonymous · Answer

i/m not sure how to find that

mathstudent55 · Answer

We need to find the point on the base where the medians intersect each other.

mathstudent55 · Answer

That point is the centroid of the triangle.
The centroid of a triangle is where the three medians intersect.
Also, the centroid divides each median into two segments in a 2:3 ratio of lengths.

mathstudent55 · Answer

The longer segment is near the vertex.

mathstudent55 · Answer

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