To find the total area of the shape, we need to calculate the area of each simple polygon and then add them together.
1. Area of the rectangle:
Area = length x width
Area = (6 + 3 + 6) x (3)
Area = 15 x 3
Area = 45 square inches
2. Area of the two squares:
Area = side x side
Area = 3 x 3
Area = 9 square inches (per square)
Total area for two squares = 9 x 2 = 18 square inches
3. Area of the three trapezoids:
For each trapezoid, we can use the formula for the area of a trapezoid:
Area = 1/2 x (a + b) x h
Area = 1/2 x (6 + 3) x 1.2
Area = 1/2 x 9 x 1.2
Area = 5.4 square inches (per trapezoid)
Total area for three trapezoids = 5.4 x 3 = 16.2 square inches
Adding all the areas together:
Total area = 45 (rectangle) + 18 (two squares) + 16.2 (three trapezoids)
Total area = 79.2 square inches
Therefore, 79.2 square inches of cardboard are needed to make the cube.
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
1 answer