Question
urface Area of Rectangular Pyramids Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. Use the net to derive the a formula for the surface area (SA) of the rectangular pyramid. (Use the variable Abase for the area of the base, Aface 1 for the area of face 1, and Aface 2 for the area of face 2.) (1 point) Responses SA=Abase+2×Aface 1+2×Aface 2 cap s cap A is equal to cap A sub b A s e plus 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2 SA=Abase+Aface 1+Aface 2 cap s cap A is equal to cap A sub b A s e plus cap A sub f A c e 1 plus cap A sub f A c e 2 SA=2×Aface 1+2×Aface 2 cap s cap A is equal to 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2 SA=2×Abase+2×Aface 1+2×Aface 2 cap s cap A is equal to 2 times cap A sub b A s e plus 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2 Skip to navigation
Answers
GPT-4o mini
To derive the formula for the surface area (SA) of a rectangular pyramid, we consider the components of its net.
1. **Area of the Base (Abase)**: The surface area will include the area of the base, which is rectangular.
2. **Area of the Faces**: There are four triangular faces (two pairs of congruent triangles):
- The faces corresponding to the length of the base (let’s call their area Aface 1).
- The faces corresponding to the width of the base (let’s call their area Aface 2).
Hence, the total surface area of the pyramid can be expressed as:
\[
SA = Abase + 2 \times Aface_1 + 2 \times Aface_2
\]
Thus, the correct option that represents the surface area of the rectangular pyramid based on the net and utilizing the given variables is:
\[
SA = Abase + 2 \times Aface_1 + 2 \times Aface_2
\]
This matches the first response you provided.
1. **Area of the Base (Abase)**: The surface area will include the area of the base, which is rectangular.
2. **Area of the Faces**: There are four triangular faces (two pairs of congruent triangles):
- The faces corresponding to the length of the base (let’s call their area Aface 1).
- The faces corresponding to the width of the base (let’s call their area Aface 2).
Hence, the total surface area of the pyramid can be expressed as:
\[
SA = Abase + 2 \times Aface_1 + 2 \times Aface_2
\]
Thus, the correct option that represents the surface area of the rectangular pyramid based on the net and utilizing the given variables is:
\[
SA = Abase + 2 \times Aface_1 + 2 \times Aface_2
\]
This matches the first response you provided.