To find the surface area of a rectangular pyramid, we need to calculate both the area of the base and the area of the four triangular faces.
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Calculate the area of the base: The base is a rectangle with dimensions:
- Length (l) = 14 cm
- Width (w) = 12 cm
\[ \text{Area of the base} = l \times w = 14 , \text{cm} \times 12 , \text{cm} = 168 , \text{cm}^2 \]
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Calculate the area of the triangular faces: The pyramid has four triangular faces, two corresponding to each dimension of the base. We can calculate the area of each triangular face separately.
For the triangular faces along the width (12 cm):
- Base of each triangle = width = 12 cm
- Height from the apex = 10.6 cm
\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 , \text{cm} \times 10.6 , \text{cm} = 63.6 , \text{cm}^2 \]
Since there are 2 such triangular faces: \[ \text{Total area for width triangles} = 2 \times 63.6 , \text{cm}^2 = 127.2 , \text{cm}^2 \]
For the triangular faces along the length (14 cm):
- Base of each triangle = length = 14 cm
- Height from the apex = 10 cm
\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 14 , \text{cm} \times 10 , \text{cm} = 70 , \text{cm}^2 \]
Since there are 2 such triangular faces: \[ \text{Total area for length triangles} = 2 \times 70 , \text{cm}^2 = 140 , \text{cm}^2 \]
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Calculate the total surface area: Now, we can add the area of the base and the areas of the triangular faces together:
\[ \text{Total Surface Area} = \text{Area of the base} + \text{Total area of width triangles} + \text{Total area of length triangles} \]
\[ \text{Total Surface Area} = 168 , \text{cm}^2 + 127.2 , \text{cm}^2 + 140 , \text{cm}^2 = 435.2 , \text{cm}^2 \]
The final answer for the surface area of the rectangular pyramid is:
435.2 cm²