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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=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

SA=Abase+Aface 1+Aface 2

the base is a rectangle in the middle, face 1 is on the top and bottom while face 2 is on the left and right

1 answer

To derive the formula for the surface area (SA) of a rectangular pyramid using the given variables, let's break down the components:

  1. Base Area (Abase): The base of the pyramid is a rectangle, so its area is represented as \( Abase \).

  2. Face Areas:

    • Face 1: These are the triangular faces corresponding to one of the dimensions of the base. Since there are two of these triangular faces, we denote their area as \( Aface_1 \).
    • Face 2: These are the triangular faces corresponding to the other dimension of the base. Similarly, there are two such triangular faces, denoted as \( Aface_2 \).

Given this breakdown, the total surface area of the pyramid (SA) can be expressed as the sum of the area of the base and the areas of the triangular faces. The formula can be summarized as:

\[ SA = Abase + 2 \times Aface_1 + 2 \times Aface_2 \]

Therefore, the correct response is:

SA = Abase + 2 × Aface 1 + 2 × Aface 2

This equation accounts for the area of the rectangular base and twice the areas of each type of triangular face.