Question

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​

Answer 1

Total surface area of the square pyramid is 1476 cm².

Explanation:

• Step 1:

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

• Step 2:

Find perimeter of the base

⇒ p = 4 × side = 4 × 6 = 24 cm

• Step 3:

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

• Step 4:

Find the area of the base of the pyramid.

⇒ B = side² = 6² = 36 cm²

• Step 5:

Calculate total surface area of the pyramid.

⇒ TSA = 12 × 24 × 5 + 36 = 1440 + 36 = 1476 cm²