A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #3 # and #7 # and the pyramid's height is #8 #. If one of the base's corners has an angle of #(3pi)/8#, what is the pyramid's surface area?
1 Answer
Explanation:
Work in the usual 3-dimensional Cartesian co-ordinate system
Then the apex of the pyramid is at
We calculate the area of the triangles on short and long sides by the usual triangle area formula:
Short sides:
Long sides:
We may take that
Thus the total surface area of the pyramid:
To three significant figures, this equals 83.0 square units. Note that I have derived an exact expression here, but it is possible that the question setter desires everything to be computed on a calculator instead, in which case we do not need to know the