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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×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=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

1 answer

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

  1. The base of the pyramid is a rectangle, so its area is represented as \( Abase \).
  2. There are two different triangular faces: "face 1" and "face 2." Each triangular face has its own area.

When calculating the total surface area, you have:

  • The area of the base: \( Abase \)
  • The area of the two triangular faces labeled "face 1," which can be represented as \( 2 \times Aface 1 \)
  • The area of the two triangular faces labeled "face 2," represented as \( 2 \times Aface 2 \)

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

\[ SA = Abase + 2 \times Aface 1 + 2 \times Aface 2 \]

Therefore, the correct response is:

SA = Abase + 2×Aface 1 + 2×Aface 2