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Question

A rectangle has 4 triangles connected to it. One triangle is attached to each side of the rectangle. The rectangle is labeled base. The triangle on the top is labeled face 1. The triangle on the right is labeled face 2. The triangle on the bottom is labeled face 1. The triangle on the left is labeled face 2.

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+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

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
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Answer 1

To derive the formula for the surface area (SA) of a rectangular pyramid using the given net, we start by identifying the components involved.

1. The base of the pyramid is a rectangle, and its area is represented as \( A_{\text{base}} \).
2. There are two triangular faces labeled as face 1 and face 2, with their areas represented as \( A_{\text{face 1}} \) and \( A_{\text{face 2}} \).
3. Since the arrangement seems to describe a rectangular pyramid, where each triangular face corresponds to the edges of the rectangle forming the sides of the pyramid, we can determine the contribution to the surface area from each of these components.

The surface area (SA) of the rectangular pyramid can be calculated by adding together the area of the base and the areas of the triangular faces. Since there are typically two triangular faces of each type (face 1 and face 2) in a rectangular pyramid (one on each side), we can summarize the surface area formula as follows:

\[ SA = A_{\text{base}} + 2 \times A_{\text{face 1}} + 2 \times A_{\text{face 2}} \]

Therefore, the correct response is:

SA = Abase + 2×Aface 1 + 2×Aface 2

This formula accounts for the base area once and the triangular face areas twice, confirming that there are two of each triangular face type due to their positions around the rectangular base.