The total height of the figure shown is 20 inches and the slant is 17 inches. which has a greater surface area, the prism or pyramid . explain

Surface area of the prism is greater than surface area of the pyramid

Step-by-step explanation:

* lets study the figure

- We have square prism, the base is a square with side length

 16 inches and height 5 inches

- We have square pyramid, the base is a square of side length

  16 inches and slant height 17 inches

- The total height of the combined shape is 20 inches

∵ The total height is 20 inches and the height of the prism is 5 inches

∴ The height of the pyramid = 20 - 5 = 15 inches

∵ The slant height and the height of the pyramid with 1/2

   side of the base make right angle triangle, The slant height

   is the hypotenuse

∵ √(8² + 15²) = √289 = 17

∴ The slant height of the pyramid = 17 inches

- This step to be sure that 17 is the slant height of the pyramid

  not the combined shape

* Lets revise the rules of the surface area of the square prism

 and the square pyramid

- Surface area of the prism = PH + 2 B.A, where

# P is the perimeter of the base

# H is the height

# B.A is the base area

∵ The base is the square

∴ P = the length of the side × 4 = 16 × 4 = 64 inches

∴ B.A = (length of the side)² = (16)² = 256 inches²

∵ H = 5

∴ S.A of the prism = 64 × 5 + 2 × 256 = 320 + 512 = 832 inches²

- Surface area of the pyramid = 1/2 PL + B.A, where

# P is the perimeter of the base

# L is the slant height

# B.A is area of the base

∵ The base is the square

∴ P = the length of the side × 4 = 16 × 4 = 64 inches

∴ B.A = (length of the side)² = (16)² = 256 inches²

∵ L = 17 inches

∴ S.A of the pyramid = 1/2 × 64 × 17 +  256 = 544 + 256 = 800 inches²

∴ Surface area of the prism > surface area of the pyramid

good luck on your studies! : )

david edward.