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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=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×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

1 answer

To derive the formula for the surface area (SA) of the rectangular pyramid, we need to consider both the area of the base and the areas of the triangular faces.

  1. The area of the base (rectangle) is represented as \( A_{\text{base}} \).
  2. Each triangular face facing up and down is labeled \( A_{\text{face 1}} \).
  3. Each triangular face on the sides is labeled \( A_{\text{face 2}} \).

The base contributes \( A_{\text{base}} \) to the surface area, while each triangular face on the base contributes as follows:

  • There are 2 triangular faces labeled \( A_{\text{face 1}} \) (one on the top and one on the bottom).
  • There are also 2 triangular faces labeled \( A_{\text{face 2}} \) (one on the right and one on the left).

Therefore, the total surface area (SA) can be expressed as:

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

Thus, the correct option for the formula for the surface area of the rectangular pyramid is:

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