A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #3 #, its base has sides of length #6 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?

1 Answer
salamat
Jan 25, 2017

#18sqrt3+36sqrt2#

Explanation:

The pyramid's surface area = base area + 4 x plane area.
Base area #=bcsin A#, where #b=6#, #c=6# and #A=pi/3#
Base area #=6*6sin(pi/3)#
#=36*sqrt3/2=18sqrt3#

Plane area, we have to find the length from peak to the mid point of side.
Since the length from mid point of side =3, and the height =3, therefore, the length from peak to the mid point of side #= sqrt(3^2+3^2)#
#=sqrt18=3sqrt2#
The area of one plane #=1/2*6*3sqrt2=9sqrt2#

Total plane area #= 4*9sqrt2=36sqrt2#

Total area of pyramid #=18sqrt3+36sqrt2#

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