Asked by Pixa

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Part 1
To find how many square feet of glass he needs to cover the entire​ pyramid, find the surface area of the square pyramid.​ First, draw and label a net of the square pyramid as shown.Question content area top
Part 1
Parker is designing a piece of artwork for a hotel. The artwork is in the shape of a square pyramid as shown. He wants to cover the pyramid with decorative glass. Use a net to find how many square feet of glass he needs to cover the entire pyramid.
3.8 ft
3 ft
Question content area bottom
Part 1
He needs
  
enter your response here ftsquared of glass to cover the entire pyramind
7 ft
8.2 ft
Part 2
​Now, find the area of each face. Since four of the faces of the pyramid are triangles that are equal in​ size, begin by finding the area of one of the triangular faces.
Part 3
Use the net and the formula Aequalsone half bh
to find the area of a triangular face.
Upper A
equals
one half bh
equals
one half left parenthesis 8.2 right parenthesis left parenthesis 7 right parenthesis
Substitute.
7 ft
8.2 ft
Part 4
Upper A
equals
28.7
Multiply.
Part 5
​Thus, the area of one triangular face is 28.7 ftsquared.
Part 6
​Next, find the area of the square face. Use the net and the formula Aequalss Superscript 2.
Upper A
equals
s Superscript 2
equals
left parenthesis 8.2 right parenthesis squared
Substitute.
7 ft
8.2 ft
Part 7
Upper A
equals
67.24
Multiply.
Part 8
The area of the square face is 67.24 ftsquared.
Part 9
​Finally, add the areas of all the faces to find the surface area of the square pyramid. Remember that the area of each triangular face is the same.
28.7plus28.7plus28.7plus28.7plus67.24equals182.04
Part 10
He needs 182.04 ftsquared of glass to cover the entire pyramid

All Answers 1

Answered by GPT-5 mini AI
Your work and arithmetic are correct.

- Area of one triangular face = (1/2)(base)(slant height) = (1/2)(8.2)(7) = 28.7 ft^2.
- Four triangles: 4 × 28.7 = 114.8 ft^2.
- Area of square base = 8.2^2 = 67.24 ft^2.
- Total surface area = 114.8 + 67.24 = 182.04 ft^2.

He needs 182.04 ft^2 of glass to cover the entire pyramid.