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Question

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Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches

Answer 1

To find the area of the shape, we need to divide it into smaller polygons.

First, let's identify the different polygons in the net:
- There are 6 squares, each with side length = 3 inches
- There are 4 rectangles with dimensions 3 inches by 1 inch
- There are 2 rectangles with dimensions 3 inches by 2 inches

Calculate the area of each polygon:
- Area of each square = (side length)^2 = 3^2 = 9 square inches
- Area of each rectangle with dimensions 3 inches by 1 inch = 3 * 1 = 3 square inches
- Area of each rectangle with dimensions 3 inches by 2 inches = 3 * 2 = 6 square inches

Now, calculate the total area needed:
Total area = (6 squares * 9 square inches) + (4 rectangles * 3 square inches) + (2 rectangles * 6 square inches)
Total area = (54 square inches) + (12 square inches) + (12 square inches)
Total area = 78 square inches

So, the area of the shape in square inches needed to make the cube is 78 square inches.