To find the surface area of the rectangular pyramid, we can use the formula:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area} \]
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Calculate the Base Area: The base of the pyramid is rectangular and its area can be calculated as:
\[ \text{Base Area} = \text{length} \times \text{width} = 20 , \text{cm} \times 18 , \text{cm} = 360 , \text{cm}^2 \]
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Calculate the Lateral Surface Area: The pyramid has 4 triangular faces. We will calculate the area of each triangular face individually.
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Lateral face 1 (with the height of 16.6 cm): The area of the triangular face can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangles using the length 20 cm as base:
\[ \text{Area}_1 = \frac{1}{2} \times 20 , \text{cm} \times 16.6 , \text{cm} = 166 , \text{cm}^2 \]
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Lateral face 2 (also with the height of 16.6 cm): This triangular face also has a base of 20 cm:
\[ \text{Area}_2 = 166 , \text{cm}^2 \]
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Lateral face 3 (with the height of 17.2 cm): Now we will use the width of the base (18 cm) for this triangular face:
\[ \text{Area}_3 = \frac{1}{2} \times 18 , \text{cm} \times 17.2 , \text{cm} = 154.8 , \text{cm}^2 \]
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Lateral face 4 (also with the height of 17.2 cm): This triangular face also has a base of 18 cm:
\[ \text{Area}_4 = 154.8 , \text{cm}^2 \]
Now, we can sum the areas of all four triangular faces to find the total lateral surface area:
\[ \text{Total Lateral Surface Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 + \text{Area}_4 \] \[ = 166 , \text{cm}^2 + 166 , \text{cm}^2 + 154.8 , \text{cm}^2 + 154.8 , \text{cm}^2 \] \[ = 642.4 , \text{cm}^2 \]
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Calculate the Total Surface Area: Now, we can add the base area and the lateral surface area:
\[ \text{Surface Area} = 360 , \text{cm}^2 + 642.4 , \text{cm}^2 = 1002.4 , \text{cm}^2 \]
None of the provided options exactly matches our calculated total area of 1002.4 cm². However, if we round this or consider possible small calculation variations, the closest response is 1,001.6 cm².
Thus, the answer is:
1,001.6 cm²