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 #5 #, its base has sides of length #8 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?
Area of rombus base with each side
The rhombus base of pyramid has its semi-diagonals
Now, the sides of triangular lateral face of pyramid as given as
Each of 4 identical lateral triangular faces of pyramid has the sides
semi-perimeter of triangle,
Now, using heron's formula the area of lateral triangular face of pyramid
Hence, the total surface area of pyramid