Find the total surface area of a square based prism (cuboid) of height 4cm, given that the side length of its base is 6cm.
please show working out

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

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Step-by-step explanation: