You need 400 cm² of paper.
Step-by-step explanation:
Step 1:
To determine the amount of paper needed to cover the entire shape, we need to determine the surface area of the entire shape.
The shape consists of a rectangular prism and a square pyramid on top of it.
We need to determine the areas of all the external sides to determine the total surface area.
Step 2:
The external shape consists of 1 square (base of the prism), 4 rectangles (sides of the prism), and 4 triangles (sides of the pyramid).
The square has a side length of 8cm. So
The area of the square [tex]= 8^{2} = 64[/tex] cm².
The rectangles have lengths of 8 cm and widths of 7 cm.
The area of 4 rectangles [tex]= 4 (8)(7) = 4(56) = 224[/tex] cm².
The triangles have base lengths of 8 cm and heights of 7 cm.
The area of 4 triangles [tex]= 4 (\frac{1}{2} (8)(7)) = (28)4 = 112[/tex] cm².
Step 3:
The total surface area of the prism = The area of the square + The area of 4 rectangles + The area of 4 triangles.
The total surface area[tex]= 64 + 224 + 112 = 400[/tex] cm².
So 400 cm² of paper is needed to cover the entire shape.
