To find the total area of the shape, we need to calculate the area of each individual polygon and then add them up.
1. Rectangle: The area is length times width, so for the rectangle it would be 6 x 3 = 18 square inches.
2. Squares: Each square has a side length of 3, so the area of one square is 3 x 3 = 9 square inches. Since there are two squares, the total area for the squares is 2 x 9 = 18 square inches.
3. Trapezoids: There are 3 trapezoids with different dimensions. To find the area of each trapezoid, we use the formula: ((a + b) * h) / 2.
- Trapezoid 1 (top left): ((3 + 1.2) * 3) / 2 = (4.2 * 3) / 2 = 6.3 square inches
- Trapezoid 2 (top right): ((3 + 1.2) * 3) / 2 = (4.2 * 3) / 2 = 6.3 square inches
- Trapezoid 3 (bottom): ((6 + 3) * 3) / 2 = (9 * 3) / 2 = 13.5 square inches
Now, we add up the areas of all the polygons:
Rectangle: 18 square inches
Squares: 18 square inches
Trapezoids: 6.3 + 6.3 + 13.5 = 26.1 square inches
Total area: 18 + 18 + 26.1 = 62.1 square inches
So, the total cardboard needed to make the cube is 62.1 square inches.
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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2 answers
Use the image to answer the question.
An illustration shows an outline of a right arrow consisting of a rectangle and a triangular head to its right. The length of the rectangle is 4 and the width is 2. The right width of the triangle does not show a line. It forms the central part of the verticle base of the triangle. The other parts of the base are labeled 2 on the top and bottom each. The perpendicular height from the base to the top vertex of the triangle is labeled as 5.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?
An illustration shows an outline of a right arrow consisting of a rectangle and a triangular head to its right. The length of the rectangle is 4 and the width is 2. The right width of the triangle does not show a line. It forms the central part of the verticle base of the triangle. The other parts of the base are labeled 2 on the top and bottom each. The perpendicular height from the base to the top vertex of the triangle is labeled as 5.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?