To calculate the surface area of a rectangular pyramid, we need to find the area of the base and the areas of the four triangular faces.
Given:
- Width (b) = 20 cm
- Length (l) = 18 cm
- Slant height on the front (sl_f) = 16.5 cm
- Slant height on the right (sl_r) = 17.2 cm
Steps to Calculate Surface Area:
1. Area of the Base:
The base of the pyramid is a rectangle.
\[ \text{Area of base} = \text{length} \times \text{width} = l \times b = 18 , \text{cm} \times 20 , \text{cm} = 360 , \text{cm}^2 \]
2. Area of the Triangular Faces:
-
Front Face: \[ \text{Area}_{\text{front}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b \times sl_f = \frac{1}{2} \times 20 , \text{cm} \times 16.5 , \text{cm = 165 , cm}^2 \]
-
Back Face: (This will have the same area as the front face.) \[ \text{Area}_{\text{back}} = \frac{1}{2} \times b \times sl_f = 165 , \text{cm}^2 \]
-
Left Face: \[ \text{Area}_{\text{left}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times l \times sl_r = \frac{1}{2} \times 18 , \text{cm} \times 17.2 , \text{cm} = 154.8 , \text{cm}^2 \]
-
Right Face: (This will have the same area as the left face.) \[ \text{Area}_{\text{right}} = \frac{1}{2} \times l \times sl_r = 154.8 , \text{cm}^2 \]
3. Total Surface Area:
Now, add the area of the base and the areas of the four triangular faces:
\[ \text{Total Surface Area} = \text{Area of base} + \text{Area}{\text{front}} + \text{Area}{\text{back}} + \text{Area}{\text{left}} + \text{Area}{\text{right}} \]
\[ \text{Total Surface Area} = 360 , \text{cm}^2 + 165 , \text{cm}^2 + 165 , \text{cm}^2 + 154.8 , \text{cm}^2 + 154.8 , \text{cm}^2 \]
\[ \text{Total Surface Area} = 360 + 165 + 165 + 154.8 + 154.8 = 1000.6 , \text{cm}^2 \]
Conclusion:
The total surface area of the rectangular pyramid is approximately 1,001.6 cm².
Thus, the correct response is: 1,001.6 cm² (1,001.6 cm squared).