To calculate the surface area of the rectangular pyramid, we need to find both the area of the base and the areas of the triangular lateral faces.
-
Area of the Base: The base is rectangular with dimensions:
- Length (L) = 20 cm
- Width (W) = 18 cm
The area of the base (A_base) is calculated as: \[ A_{\text{base}} = L \times W = 20 , \text{cm} \times 18 , \text{cm} = 360 , \text{cm}^2 \]
-
Lateral Faces: There are four triangular lateral faces. We need to find the area of each triangular face.
-
For the triangular face opposite the length (20 cm), we use:
- Base = 20 cm
- Height = 17.2 cm (perpendicular height from the apex)
The area of this triangular face (A_triangle1) is: \[ A_{\text{triangle1}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 , \text{cm} \times 17.2 , \text{cm} = 172 , \text{cm}^2 \]
-
The same calculation applies for the opposite triangular face (it shares the same dimensions), so: \[ A_{\text{triangle2}} = 172 , \text{cm}^2 \]
-
For the triangular face opposite the width (18 cm), we use:
- Base = 18 cm
- Height = 16.6 cm (perpendicular height from the apex)
The area of this triangular face (A_triangle3) is: \[ A_{\text{triangle3}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 , \text{cm} \times 16.6 , \text{cm} = 149.4 , \text{cm}^2 \]
-
The same calculation applies for the opposite triangular face, so: \[ A_{\text{triangle4}} = 149.4 , \text{cm}^2 \]
-
-
Total Area of Lateral Faces: The total area of the lateral faces (A_lateral) is: \[ A_{\text{lateral}} = 2 \times A_{\text{triangle1}} + 2 \times A_{\text{triangle3}} = 2 \times 172 , \text{cm}^2 + 2 \times 149.4 , \text{cm}^2 = 344 , \text{cm}^2 + 298.8 , \text{cm}^2 = 642.8 , \text{cm}^2 \]
-
Total Surface Area of the Pyramid: The total surface area (A_total) is given by: \[ A_{\text{total}} = A_{\text{base}} + A_{\text{lateral}} = 360 , \text{cm}^2 + 642.8 , \text{cm}^2 = 1002.8 , \text{cm}^2 \]
Based on the options given, the closest match is 1,001.6 cm².
Thus, the correct response is: 1,001.6 cm²