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 #7 #, its base's sides have lengths of #1 #, and its base has a corner with an angle of #(5 pi)/8 #. What is the pyramid's surface area?
1 Answer
Pyramid surface area
Explanation:
We need to calculate the edges of the lateral faces of the pyramid. We start by calculating the diagonals of the base.
By Cosine Law with base side
Let diagonal
diagonal
diagonal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let diagonal
diagonal
diagonal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Compute for the lateral edges
compute c:
Compute for the Areas of the base, and Lateral faces.
For the Rhombus base:
For the Lateral Face Area
start with the half-perimeter
~~~~~~~~~~~~~~~~~~~~~~~~
Surface Area of the Pyramid
God bless....I hope the explanation is useful.