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
To find the total area of the shape, we need to first find the area of each individual polygon and then add them up.
Area of rectangle = length x width
Area of rectangle = (6 + 3 + 3) x 6
Area of rectangle = 12 x 6
Area of rectangle = 72 square inches
Area of each trapezoid = ((base1 + base2) / 2) x height
Area of shaded trapezoids = ((3 + 6) / 2) x 1
Area of shaded trapezoids = (9 / 2) x 1
Area of shaded trapezoids = 4.5 square inches each
Area of each square = side x side
Area of square = 3 x 3
Area of square = 9 square inches each
Now let's add the total area of all the polygons:
Rectangle + 2(trapezoids) + 2(squares)
72 + 2(4.5) + 2(9)
72 + 9 + 18
99 square inches
Therefore, the total area of the shape is 99 square inches.