To find the surface area (S.A.) of a triangular prism, we need to calculate the areas of the two triangle bases and the three rectangular sides.
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Find the area of the triangular base:
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We can use the formula for the area of a triangle:
\[ \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} \] -
The base of the triangle is the width (W = 27.9 cm) and the height (H = 5.1 cm).
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So, \[ \text{Area} = \frac{1}{2} \times 27.9 , \text{cm} \times 5.1 , \text{cm} = \frac{1}{2} \times 27.9 \times 5.1 = 71.145 , \text{cm}^2 \]
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Calculate the area of the two triangular bases: \[ \text{Area of two triangles} = 2 \times 71.145 , \text{cm}^2 = 142.29 , \text{cm}^2 \]
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Find the area of the three rectangular faces:
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The three rectangular sides are:
- Rectangle 1 (base × length): \( 27.9 , \text{cm} \times 30.5 , \text{cm} \)
- Rectangle 2 (slant height × length): \( 28.4 , \text{cm} \times 30.5 , \text{cm} \)
- Rectangle 3 (height × length): \( 5.1 , \text{cm} \times 30.5 , \text{cm} \)
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Calculating these areas:
- Rectangle 1: \[ 27.9 , \text{cm} \times 30.5 , \text{cm} = 850.95 , \text{cm}^2 \]
- Rectangle 2: \[ 28.4 , \text{cm} \times 30.5 , \text{cm} = 867.2 , \text{cm}^2 \]
- Rectangle 3: \[ 5.1 , \text{cm} \times 30.5 , \text{cm} = 155.55 , \text{cm}^2 \]
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Total area of the rectangular sides: \[ \text{Total area} = 850.95 , \text{cm}^2 + 867.2 , \text{cm}^2 + 155.55 , \text{cm}^2 = 1873.7 , \text{cm}^2 \]
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Total surface area of the prism: \[ \text{Total Surface Area} = \text{Area of two triangles} + \text{Total area of rectangular sides} \] \[ \text{Total Surface Area} = 142.29 , \text{cm}^2 + 1873.7 , \text{cm}^2 = 2016 , \text{cm}^2 , (\text{rounded to nearest whole number}) \]
Therefore, the surface area required to wrap the toy is 2016 cm².