Questions: (a) Find the following side lengths for the net. A=7 mm B=10 mm C=4 mm D=4 mm (b) Use the net to find the surface area of the prism. mm^2

Solution Steps

The dimensions of the prism are given as follows:

• \( A = 7 \, \text{mm} \)
• \( B = 10 \, \text{mm} \)
• \( C = 4 \, \text{mm} \)
• \( D = 4 \, \text{mm} \)

Calculate the area of each face of the prism:

• Area of face 1 (rectangle with dimensions \( A \) and \( B \)): \[ \text{Area}_{1} = A \times B = 7 \times 10 = 70 \, \text{mm}^2 \]
• Area of face 2 (rectangle with dimensions \( A \) and \( C \)): \[ \text{Area}_{2} = A \times C = 7 \times 4 = 28 \, \text{mm}^2 \]
• Area of face 3 (rectangle with dimensions \( B \) and \( C \)): \[ \text{Area}_{3} = B \times C = 10 \times 4 = 40 \, \text{mm}^2 \]

The total surface area \( S \) of the prism is calculated by summing the areas of all faces, considering that opposite faces are equal: \[ S = 2 \times (\text{Area}_{1} + \text{Area}_{2} + \text{Area}_{3}) = 2 \times (70 + 28 + 40) = 2 \times 138 = 276 \, \text{mm}^2 \]

Final Answer