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Question

All edges of a square pyramid are of equal lengths. If the length of the base edge is 20 cm, what is the total surface area?

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Solution

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=103

Now, Lateral surface area of the pyramid = 2×20×103=4003

Substituting the values in (i)

Total surface area of the pyramid = 400+4003=400(1+3)


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