Answer:
Explanation:
First is to find area of base triangle:
It is an equilateral triangle with one side at 4
Height is given by 4*sin60degree = 2*sqrt(3)
Area = 1/2 * side * height
= 1/2*2*sqrt(3)*4
= 4*sqrt(3)
Height of pyramid is at centroid of the base equilateral triangle
Length of angle bisector of the base equilateral triangle
= sqrt(4^2 - 2^2)
= sqrt(16-4)
= sqrt(12)
Centroid is at sqrt(12)/3 from the nearest side.
Consider right-angle triangle formed by top of pyramid and centroid:
Height^2 + (sqrt(12)/3)^2 = 4^2 - 2^2
Height^2 = 16 - 12 - 12/9 = 24/9
Height = (2/3)*sqrt(6)
Volume of pyramid = 1/3*base area*height
= 1/3*4*sqrt(3)*(2/3)*sqrt(6)
= (8/3)*sqrt(2)
= 3.77