# 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 #2 #, and its base has a corner with an angle of # pi/4 #. What is the pyramid's surface area?

T S A = 19.0133

AB = BC = CD = DA = a = 2

Height OE = h = 3

OF = a/2 = 1/2 = 1

Area of

Lateral surface area

diagonal

#OB = d_2/2 = BC*sin (C/2)=3*sin(pi/8)= 1.1481

#OC = d_1/2 = BC cos (C/2) = 3* cos (pi/8) = 2.7716

Area of base ABCD

T S A

T S A

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The surface area of the pyramid is ( 12\sqrt{2} + 6\sqrt{3} ) square units.

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