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?

33.6 38.1 and 55 are all not right

Answer 1

[AI-generated answer — Bot GPT 3.5]

The area of the shape can be found by summing the areas of each individual polygon that makes up the box net.

1. Rectangle:
The area of the rectangle is length x width.
Area = 6 x 6 = 36 square inches

2. Two squares:
Each square has a side length of 3.
Area of each square = side x side = 3 x 3 = 9 square inches
Total area of both squares = 2 x 9 = 18 square inches

3. Four trapezoids:
Each trapezoid can be divided into a rectangle and a right triangle.
Top trapezoids:
Area = (3 + 3) x 1 / 2 = 6 x 1 / 2 = 3 square inches each
Total area = 2 x 3 = 6 square inches

Short side trapezoid:
Area = (3 + 1.2) x 1 / 2 = 4.2 x 1 / 2 = 2.1 square inches

Long side trapezoid:
Area = (6 + 3) x 1 / 2 = 9 x 1 / 2 = 4.5 square inches each
Total area = 2 x 4.5 = 9 square inches

Total area = 36 + 18 + 6 + 2.1 + 9 = 71.1 square inches

Therefore, the cardboard needed to make the cube is 71.1 square inches.

Answer 2

are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake in my previous response. Let's recalculate the area of the shape.

1. The rectangle:
Area = 6 x 6 = 36 square inches

2. Two squares:
Area of each square = 3 x 3 = 9 square inches
Total area of both squares = 2 x 9 = 18 square inches

3. Four trapezoids:
Top trapezoids:
Area = ((3 + 6) / 2) x 1 = 4.5 x 1 = 4.5 square inches each
Total area = 2 x 4.5 = 9 square inches

Short side trapezoid:
Area = ((1.2 + 3) / 2) x 3 = 2.1 x 3 = 6.3 square inches

Long side trapezoid:
Area = ((3 + 6) / 2) x 3 = 4.5 x 3 = 13.5 square inches each
Total area = 2 x 13.5 = 27 square inches

Total area = 36 + 18 + 9 + 6.3 + 27 = 96.3 square inches

Therefore, the correct amount of cardboard needed to make the cube is 96.3 square inches. Thank you for bringing this to my attention.