Question

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Explanation:

Problem 9:

Step 1: Identify the shapes (rectangles)

We have three types of rectangles? Wait, no, looking at the net, it's a rectangular prism net. Let's find the dimensions. The length, width, height: let's see the sides. From the net, the dimensions are length \( l = 14 \), width \( w = 10 \), height \( h = 7 \)? Wait, no, let's check the areas. Wait, the net has different rectangles. Let's list the areas of each face.

Wait, the net for a rectangular prism has 6 faces: 2 of each pair. Let's see the first net (problem 9):

Looking at the rectangles:

• Two rectangles with dimensions \( 14 \times 7 \)
• Two rectangles with dimensions \( 14 \times 10 \)
• Two rectangles with dimensions \( 10 \times 7 \)

Wait, no, let's check the given numbers. The first column: 14 (height), 7 (width), then 10 (length)? Wait, maybe better to calculate each face area.

Wait, the formula for the surface area of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l \), \( w \), \( h \) are length, width, height.

Let's identify \( l \), \( w \), \( h \) from the net:

From the net, the three different dimensions: 14, 10, 7. So let's take \( l = 14 \), \( w = 10 \), \( h = 7 \).

Step 2: Calculate each pair of faces

• Area of \( lw \) (length × width): \( 14 \times 10 = 140 \), two of these: \( 2 \times 140 = 280 \)
• Area of \( lh \) (length × height): \( 14 \times 7 = 98 \), two of these: \( 2 \times 98 = 196 \)
• Area of \( wh \) (width × height): \( 10 \times 7 = 70 \), two of these: \( 2 \times 70 = 140 \)

Step 3: Sum the areas

Total surface area \( SA = 280 + 196 + 140 = 616 \)

Wait, let's verify with the net. The net has:

• Two rectangles with 14 and 7: \( 14 \times 7 = 98 \), two of them: \( 2 \times 98 = 196 \)
• Two rectangles with 14 and 10: \( 14 \times 10 = 140 \), two of them: \( 2 \times 140 = 280 \)
• Two rectangles with 10 and 7: \( 10 \times 7 = 70 \), two of them: \( 2 \times 70 = 140 \)

Summing these: \( 196 + 280 + 140 = 616 \)

Step 1: Identify the dimensions

The net for problem 10: let's find the dimensions. The net has rectangles with dimensions:

Looking at the net, the dimensions are:

• Two rectangles with \( 12 \times 15 \)
• Two rectangles with \( 12 \times 11 \)
• Two rectangles with \( 15 \times 11 \)

Wait, the formula for surface area of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l = 15 \), \( w = 11 \), \( h = 12 \)? Wait, let's check the dimensions.

From the net, the three different rectangles:

• \( 12 \times 15 \) (two of these)
• \( 12 \times 11 \) (two of these)
• \( 15 \times 11 \) (two of these)

So let's calculate each pair:

• Area of \( 12 \times 15 \): \( 180 \), two of them: \( 2 \times 180 = 360 \)
• Area of \( 12 \times 11 \): \( 132 \), two of them: \( 2 \times 132 = 264 \)
• Area of \( 15 \times 11 \): \( 165 \), two of them: \( 2 \times 165 = 330 \)

Step 2: Sum the areas

Total surface area \( SA = 360 + 264 + 330 = 954 \)

Wait, let's verify with the formula \( SA = 2(lw + lh + wh) \), where \( l = 15 \), \( w = 11 \), \( h = 12 \):

\( lw = 15 \times 11 = 165 \)

\( lh = 15 \times 12 = 180 \)

\( wh = 11 \times 12 = 132 \)

Then \( SA = 2(165 + 180 + 132) = 2(477) = 954 \). Correct.

Answer:

(Problem 9): 616

Problem 10: