The surface area \( S \) of a rectangular pyramid can be calculated using the formula:
\[ S = A_{\text{base}} + A_1 + A_2 + A_3 + A_4 \]
Where:
- \( A_{\text{base}} \) is the area of the base (rectangular).
- \( A_1, A_2, A_3, A_4 \) are the areas of the triangular faces.
For a rectangular base with length \( l \) and width \( w \), the area of the base is:
\[ A_{\text{base}} = l \times w \]
To find the areas of the triangular faces, you would need the heights of the triangular faces leading to each vertex of the base. Assuming you denote the heights of the triangular faces as \( h_1, h_2, h_3, \text{ and } h_4 \), the areas of the triangular faces can be calculated as follows:
- Area of triangular face 1: \( A_1 = \frac{1}{2} \times l \times h_1 \)
- Area of triangular face 2: \( A_2 = \frac{1}{2} \times w \times h_2 \)
- Area of triangular face 3: \( A_3 = \frac{1}{2} \times l \times h_3 \)
- Area of triangular face 4: \( A_4 = \frac{1}{2} \times w \times h_4 \)
Putting it all together, we have:
\[ S = A_{\text{base}} + A_1 + A_2 + A_3 + A_4 \]
Thus, the total formula for the surface area becomes:
\[ S = lw + \frac{1}{2} \times l \times h_1 + \frac{1}{2} \times w \times h_2 + \frac{1}{2} \times l \times h_3 + \frac{1}{2} \times w \times h_4 \]
Make sure to replace the heights \( h_1, h_2, h_3, h_4 \) with the appropriate measurements based on your specific pyramid.