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