Area and Volume Unit Test
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
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To find the area of the shape, we need to find the area of each individual polygon in the net and then add them up.
1. The rectangle in the center has dimensions 6x3, so the area is 6 * 3 = 18 square inches.
2. The two squares have sides of length 3, so the area of each square is 3 * 3 = 9 square inches. Since there are two squares, the total area for both squares is 2 * 9 = 18 square inches.
3. The trapezoid on the left has a base of 3, a top side of 1.2, and a height of 1. The area of a trapezoid is calculated by the formula: 1/2 * (base1 + base2) * height. Using this formula, the area of the trapezoid is 1/2 * (3 + 1.2) * 1 = 2.1 square inches.
Adding up the areas of all the polygons: 18 + 18 + 2.1 = 38.1 square inches.
Therefore, the area of the shape in square inches is 38.1 square inches.