Total surface area of the square pyramid is 1476 cm².
Step-by-step explanation:
Total surface area of a pyramid = 12pl + B. Here p is perimeter of the base which is a square = 4 × side, l is the slant height and B is the area of the base = side²
Find perimeter of the base
⇒ p = 4 × side = 4 × 6 = 24 cm
Find the slant height of the prism. l² = height² + (side/2)² (Based on Pythagoras Theorem)
⇒ l² = 4² + (6/2)² = 16 + 9 = 25
⇒ l = √25 = 5 cm
Find the area of the base of the pyramid.
⇒ B = side² = 6² = 36 cm²
Calculate total surface area of the pyramid.
⇒ TSA = 12 × 24 × 5 + 36 = 1440 + 36 = 1476 cm²
