Total surface area of the pyramid = The lateral surface area of a square pyramid + Area of the square face of the pyramid
⇒ T.S.A of pyramid = 4× Area of a triangular face of the pyramid + Area of the square face of the pyramid
⇒ T.S.A of pyramid = 4×12×Base edge of the triangle×Slant height of the pyramid + Area of the square face of the pyramid ......(i)
Given that Length of the base edge= Length of the lateral edge= 20 cm.
Thus, Base area = 20×20=400
Note that Slant height of the pyramid= √(Lateral edge)2−(Half the base edge)2=√(20)2−(10)2=10√3
Now, Lateral surface area of the pyramid = 2×20×10√3=400√3
Substituting the values in (i)
Total surface area of the pyramid = 400+400√3=400(1+√3)