To derive a formula for the surface area (SA) of a rectangular pyramid, we need to understand what components make up the surface area. A rectangular pyramid consists of a rectangular base and four triangular faces.
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Base Area (Abase): The base of the pyramid is a rectangle, and we denote its area as \( A_{base} \).
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Face Areas (Aface1 and Aface2): The pyramid has four triangular faces. If we denote the area of two distinct face types as \( A_{face 1} \) and \( A_{face 2} \), it is common to have two of the same face area (for the two triangular faces that share the same dimension) and possibly two other triangles of a different size or shape (depending on the base dimensions).
Let's break down the surface area:
- You have one rectangular base with area \( A_{base} \).
- You typically have two pairs of triangular faces. If we denote the areas of these faces as \( A_{face 1} \) and \( A_{face 2} \), then the contribution of the triangular faces to the surface area will emit the total areas of these faces.
Therefore, the complete formula for the surface area is:
\[ SA = A_{base} + 2 \cdot A_{face 1} + 2 \cdot A_{face 2} \]
This formula accounts for one base area and two triangular faces, each counted twice (since there are two of each type).
From your provided options, the correct one is:
SA = Abase + 2×Aface 1 + 2×Aface 2