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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

1 answer

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.