Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make cube. Assume that all angles that look like a right triangle are right triangles. All Polygons that look congruent are congruent. What is the area of the shape in square inches?
To find the total area of the shape in square inches, we need to find the area of each individual polygon in the box net.
1. The top square of the cube has side length 6 inches, so its area is 6 * 6 = 36 square inches.
2. The bottom square is the same size as the top square, so its area is also 36 square inches.
3. The four side rectangles have dimensions of 6 inches by 4 inches, so each has an area of 6 * 4 = 24 square inches. Since there are four of them, the total area of the side rectangles is 24 * 4 = 96 square inches.
4. The two smaller rectangles have dimensions of 4 inches by 4 inches, so each has an area of 4 * 4 = 16 square inches. Since there are two of them, the total area of the smaller rectangles is 16 * 2 = 32 square inches.
Adding up the areas of all the polygons, we get:
36 (top square) + 36 (bottom square) + 96 (side rectangles) + 32 (smaller rectangles) = 200 square inches.
Therefore, 200 square inches of cardboard are needed to make the cube.