Question

Use the net of the rectangular prism to calculate the area of each face.(6 points)

Answer 1

To find the area of each face of a rectangular prism using its net, you first need to know the dimensions (length, width, and height) of the prism. The net of a rectangular prism consists of 6 rectangular faces that correspond to the sides of the prism.

Assuming the rectangular prism has the following dimensions:
- Length \(L\)
- Width \(W\)
- Height \(H\)

The areas of the faces can be calculated as follows:

1. **Front and Back Faces**: These faces are rectangles with dimensions \(L \times H\).
- Area of each front/back face = \(L \times H\)
- Total area for front and back faces = \(2 \times (L \times H)\)

2. **Left and Right Faces**: These faces are rectangles with dimensions \(W \times H\).
- Area of each left/right face = \(W \times H\)
- Total area for left and right faces = \(2 \times (W \times H)\)

3. **Top and Bottom Faces**: These faces are rectangles with dimensions \(L \times W\).
- Area of each top/bottom face = \(L \times W\)
- Total area for top and bottom faces = \(2 \times (L \times W)\)

### Summary of Areas:
- Area of front/back faces = \(2(L \times H)\)
- Area of left/right faces = \(2(W \times H)\)
- Area of top/bottom faces = \(2(L \times W)\)

### Total Surface Area:
The total surface area \(A\) of the rectangular prism can be calculated by adding up the areas of all the faces:
\[
A = 2(L \times H) + 2(W \times H) + 2(L \times W)
\]

If you have specific dimensions for \(L\), \(W\), and \(H\), substitute those values into the formulas above to calculate the area of each face.