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?
To find the area of the shape, we first need to decompose the box net into simple polygons.
The box net consists of 6 squares and 12 rectangles. Each square has an area of 1 square inch (since each side is 1 inch).
There are 12 rectangles in the box net. Four of these rectangles have sides of length 1 inch by 2 inches, giving an area of 2 square inches each. The other eight rectangles have sides of length 1 inch by 1 inch, giving an area of 1 square inch each.
So, the total area of the shape is:
6 squares * 1 square inch/square + 4 rectangles * 2 square inches/rectangle + 8 rectangles * 1 square inch/rectangle = 6 + 8 + 8 = 22 square inches.
Therefore, 22 square inches of cardboard are needed to make the cube.