Use the image to answer the question.

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.)

Responses

SA=2×Aface 1+2×Aface 2

SA=Abase+Aface 1+Aface 2

SA=2×Abase+2×Aface 1+2×Aface 2

SA=Abase+2×Aface 1+2×Aface 2

Answer 1

To derive the surface area (SA) of the rectangular pyramid based on the description provided, we need to consider both the base area and the areas of the triangular faces.

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

2. Triangular Faces:

   • There are two triangular faces labeled as face 1, which are on the top and bottom sides of the rectangle. If we denote their area as \( Aface , 1 \), then the total contribution from these two triangular faces is \( 2 \times Aface , 1 \).
   • There are also two triangular faces labeled as face 2, which are on the right and left sides of the rectangle. If we denote their area as \( Aface , 2 \), then the total contribution from these triangular faces is \( 2 \times Aface , 2 \).

Putting this all together, the surface area (SA) can be expressed as:

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

Thus, the correct choice from the options provided is:

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