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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=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
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

1 answer

To derive the formula for the surface area (SA) of the rectangular pyramid based on the description provided:

  1. The area of the base (rectangle) is denoted as Abase.
  2. The areas of the triangular faces are denoted as Aface 1 and Aface 2.
  3. The rectangular pyramid has one base area and four triangular faces. Since there are two triangles labeled as "face 1" and two triangles labeled as "face 2", we need to add the areas accordingly.

The total surface area of the pyramid is given by the sum of the area of the base and the areas of the triangular faces:

  • The base contributes: Abase
  • The triangles labeled face 1 contribute: 2 × Aface 1 (since there are two faces of this kind)
  • The triangles labeled face 2 contribute: 2 × Aface 2 (also due to having two faces of this kind)

Combining these together gives:

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

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

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

This corresponds to the option:

SA = Abase + 2×Aface 1 + 2×Aface 2.