Question

Use the image to answer the question.

An illustration shows an unfolded box net. It is comprised of a rectangle at the center, two squares extending into three trapezoids on the top and bottom, and a trapezoid on the left of the rectangle. The top side of the rectangle is labeled in three distinct sections: starting at the left, a solid line of 3 is drawn, followed by a dashed line of 3, and then a solid line of 6. The bottom of the rectangle is labeled in three distinct sections: a solid line of 6, a dashed line of 3, and a solid line of 3. The left width of the rectangle is drawn as a dashed line, labeled as 3, which becomes the base of a shaded trapezoid. The dashed lines on the top and bottom of the rectangle are extended into squares of side 3, sides drawn in dashed lines. The three outer sides of each square become the longer bases of shaded trapezoids. The top shorter side of the trapezoid is labeled as 1.2 and the perpendicular height is 1.

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?

(1 point)
___square inches

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total area of the cardboard needed to make the cube, we need to find the areas of each individual polygon and then add them up.

The rectangle in the center has dimensions of 6 by 6, so its area is 6 x 6 = 36 square inches.

The trapezoid on the left has a base of 3, a top side of 1.2, and a height of 1. To find the area of a trapezoid, we use the formula: (1/2) x (b1 + b2) x h.
So, the area of the trapezoid is (1/2) x (3 + 1.2) x 1 = 2.1 square inches.

The two trapezoids on the top and bottom each have a base of 6, a top side of 3, and a height of 1. The area of each trapezoid is (1/2) x (6 + 3) x 1 = 4.5 square inches. Since there are two of these trapezoids, the total area is 4.5 x 2 = 9 square inches.

The two squares each have a side length of 3, so the area of each square is 3 x 3 = 9 square inches. Since there are two squares, the total area is 9 x 2 = 18 square inches.

Adding up all the areas:
Rectangle: 36 square inches
Left trapezoid: 2.1 square inches
Top and bottom trapezoids: 9 square inches
Squares: 18 square inches

Total area = 36 + 2.1 + 9 + 18 = 65.1 square inches

Therefore, 65.1 square inches of cardboard is needed to make the cube.