To find the volume of the prism, we first need to determine the area of the L-shaped base and then multiply it by the height of the prism.
- Find the Area of the Base (B):
The base is L-shaped, so we can divide it into two rectangles. The measurements of the sides given are:
- Rectangle 1 has dimensions: 12 cm (length) and 8 cm (height).
- Rectangle 2 has dimensions: 10 cm (length) and 6 cm (height).
To find the area of the L-shaped base, we do the following:
Area of Rectangle 1: \[ A_1 = \text{length} \times \text{height} = 12 , \text{cm} \times 8 , \text{cm} = 96 , \text{cm}^2 \]
Area of Rectangle 2: \[ A_2 = \text{length} \times \text{height} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
- Combine the areas: Since the rectangles overlap along one edge, subtract the area of the overlap. The overlap dimensions are 6 cm by 6 cm (the shorter height of Rectangle 2 does not exceed Rectangle 1):
Area of the Overlapping Section: \[ A_{\text{overlap}} = 6 , \text{cm} \times 6 , \text{cm} = 36 , \text{cm}^2 \]
Now, the total area of the L-shaped base would be:
\[ B = A_1 + A_2 - A_{\text{overlap}} = 96 , \text{cm}^2 + 60 , \text{cm}^2 - 36 , \text{cm}^2 = 120 , \text{cm}^2 \]
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Find the Height of the Prism (h): The height of the prism is given as 3 cm.
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Calculate the Volume (V): Using the formula for the volume of a prism, \( V = B \cdot h \): \[ V = 120 , \text{cm}^2 \times 3 , \text{cm} = 360 , \text{cm}^3 \]
Final Answers:
- Area of the base, \( B = 120 , \text{cm}^2 \)
- Height of the prism, \( h = 3 , \text{cm} \)
- Volume of the prism, \( V = 360 , \text{cm}^3 \)
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