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Which figure has rotational symmetry?
An image shows four figures. Figure 1 is a crudely drawn spiral. Figure 2 is an obtuse scalene triangle. Figure 3 is a circle with an X drawn through its center. Figure 4 is a non-isosceles trapezoid.
A.
figure 1
B.
figure 2
C.
figure 3
D.
figure 4
C. figure 3
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An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
First, we need to find the surface area of each rectangular prism:
For the smaller rectangular prism on the left:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: missing information, cannot calculate
- Left and right faces: missing information, cannot calculate
For the larger rectangular prism on the right:
- Front and back faces: 6 mm x 6 mm = 36 mm² (each)
- Top and bottom faces: 6 mm x 6 mm = 36 mm² (each)
- Left and right faces: 6 mm x 8 mm = 48 mm² (each)
To find the total surface area, we need to add up the surface areas of all the faces:
80 + 80 + 36 + 36 + 48 + 48 = 328
Therefore, the total surface area of the figure is 328 square millimeters.
it says its wrong please double check ur work
I apologize for the error in my previous answer. After re-checking my calculations, I have found that I made a mistake when finding the surface area of the left rectangular prism.
The surface area of each face for the smaller rectangular prism on the left is as follows:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: 10 mm x width of the smaller rectangular prism (let's call it w) = 10w mm²
- Left and right faces: 8 mm x w = 8w mm²
The combined length of the two rectangular prisms is given as 16 mm, so we can conclude that w = 2 mm (16 mm - 6 mm - 6 mm = 4 mm, and since there are two left over lengths, each width must be 2 mm).
Therefore, the surface area of the left rectangular prism is:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: 10 mm x 2 mm = 20 mm² (each)
- Left and right faces: 8 mm x 2 mm = 16 mm² (each)
Adding up the surface areas for both rectangular prisms:
80 + 80 + 36 + 36 + 48 + 48 + 20 + 20 + 16 + 16 = 400
Hence, the total surface area of the figure is 400 square millimeters.
It also says wrong again..
I'm sorry my previous answers haven't been correct. After reviewing my calculations, I realize I made another mistake in my latest answer. Here's a step-by-step solution:
1. Find the width of the smaller rectangular prism: Since the combined length of both rectangular prisms is 16 mm and the length of the larger rectangular prism is 6 mm, then the length of the smaller rectangular prism is 16 mm - 6 mm = 10 mm. We are given that the height of the smaller rectangular prism is 8 mm. The surface area of the top and bottom faces of this smaller rectangular prism cannot be calculated without more information.
2. Calculate the surface area of the larger rectangular prism:
- Front and back faces: 6 mm x 6 mm = 36 mm² (each)
- Top and bottom faces: 6 mm x 6 mm = 36 mm² (each)
- Left and right faces: 6 mm x 8 mm = 48 mm² (each)
3. Calculate the surface area of the smaller rectangular prism:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: missing information (as determined in step 1)
- Left and right faces: missing information (as determined in step 1)
4. Add up the surface areas of both rectangular prisms:
36 + 36 + 48 + 48 + 80 + 80 = 328
Therefore, the total surface area of the three-dimensional figure is 328 square millimeters.
I apologize for any confusion the previous answers may have caused and appreciate your patience.
Thats alright. can you solve this one for me please?
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An illustration shows a three dimensional composite figure formed by a triangular prism stacked on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 32 meters, a width of 10 meters, and a height of 8 meters. The triangular prism has a rectangular base that is aligned on all edges with the rectangular prism below. The perpendicular height of the triangular prism is marked by a right angle symbol from the top vertex to the center of the triangular face. The height of the triangular face of the prism measures 12 meters. The sides of the triangular faces of the triangular prism measure 20 meters.
What is the total surface area of the figure?
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Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a triangular prism stacked on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 32 meters, a width of 10 meters, and a height of 8 meters. The triangular prism has a rectangular base that is aligned on all edges with the rectangular prism below. The perpendicular height of the triangular prism is marked by a right angle symbol from the top vertex to the center of the triangular face. The height of the triangular face of the prism measures 12 meters. The sides of the triangular faces of the triangular prism measure 20 meters.
What is the total surface area of the figure?
To find the total surface area of the figure, we need to add up the surface areas of all visible faces.
The rectangular prism has six faces, but we can only see three of them:
- Front face: 32 m x 8 m = 256 m²
- Top face: 10 m x 8 m = 80 m²
- Right face: 32 m x 10 m = 320 m²
The triangular prism also has six faces, but we can only see three of them:
- Front face: 1/2 x 20 m x 12 m = 120 m²
- Top face: missing information (not visible)
- Right face: missing information (not visible)
To find the missing dimensions, we can use the Pythagorean theorem:
12^2 + (10/2)^2 = h^2
h ≈ 12.583 m
Now we can find the surface area of the top and right faces of the triangular prism:
- Top face: 10 m x 20 m = 200 m²
- Right face: 2(1/2 x 20 m x 12.583 m) = 251.66 m²
Therefore, the total surface area of the figure is:
256 + 80 + 320 + 120 + 200 + 251.66 = 1,227.66 m²
Hence, the total surface area of the figure is approximately 1,227.66 square meters.
I think you made a mistake..
I apologize for the mistake in my previous answer.
To find the total surface area of the figure, we need to add up the surface areas of all visible faces.
The rectangular prism has six faces, but we can only see three of them:
- Front face: 32 m x 8 m = 256 m²
- Top face: 10 m x 32 m = 320 m²
- Right face: 8 m x 10 m = 80 m²
The triangular prism also has six faces, but we can only see three of them:
- Front face: 1/2 x 20 m x 12 m = 120 m²
- Top face: 32 m x 20 m = 640 m²
- Right face: 1/2 x 20 m x 15.297 m = 152.97 m²
To find the missing dimension of the triangular prism, we can use the Pythagorean theorem:
12^2 + (10/2)^2 = h^2
h ≈ 12.583 m
Therefore, the surface area of the figure is:
256 + 320 + 80 + 120 + 640 + 152.97 = 1,568.97 m²
Therefore, the total surface area of the composite figure is approximately 1,568.97 square meters.
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An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.
What is the total surface area of the figure?
To find the total surface area, we need to find the surface areas of all visible and non-visible faces, and then subtract the surface area of the missing section.
First, let's find the surface area of the larger rectangular prism:
- Front face: 15 in x 12 in = 180 in²
- Top face (before missing section): 6 in x 15 in = 90 in²
- Right face: 12 in x 6 in = 72 in²
- Back face (not visible): 15 in x 12 in = 180 in²
- Left face (not visible): 12 in x 6 in = 72 in²
- Bottom face (not visible): 6 in x 15 in = 90 in²
The total surface area of the larger rectangular prism is 594 in².
We also need to include the surface area of the missing section:
- Front face (of the missing section): 7 in x 6 in = 42 in²
- Top face (of the missing section, not visible in the larger rectangular prism): 6 in x 7 in = 42 in²
- Right face (of the missing section, not visible in the larger rectangular prism): 6 in x 12 in = 72 in²
Now we can subtract the surface area of the missing section from the total surface area of the larger rectangular prism:
594 in² - 42 in² - 42 in² - 72 in² = 438 in²
Therefore, the total surface area of the composite figure is 438 square inches.
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An illustration shows a rectangular prism with a rectangular portion removed from the bottom right. The total length is 55 inches and width is 40 inches. The length of the removed portion from the bottom right is 35 inches. The remaining width after removing the rectangular portion is 22 inches.
Nikolai is installing an L-shaped desk in his new home office. The tabletop is shown.
What is the surface area of the desktop if it is 1 in. thick?
We can start by finding the dimensions of the desktop. If the length of the rectangular portion removed from the bottom right is 35 inches and the total length of the rectangular prism is 55 inches, then the length of the remaining rectangular portion must be 20 inches (55 inches - 35 inches). Similarly, if the remaining width after removing the rectangular portion is 22 inches and the total width of the rectangular prism is 40 inches, then the width of the rectangular portion that remains must be 18 inches (40 inches - 22 inches).
Therefore, the desktop dimensions are 20 inches by 18 inches. Since the desktop is 1 inch thick, we need to add another 1 inch to each dimension, giving us a desktop size of 22 inches by 20 inches.
The surface area of the desktop is equal to the sum of the areas of the top and bottom faces plus the areas of the 4 side faces. Since the desk is L-shaped, two of the sides are not visible and two of the sides (front and right) are visible.
The surface area of the top and bottom faces is equal to the area of one face multiplied by 2, or:
2(22 in x 20 in) = 880 in²
The surface area of the front and right faces is equal to the area of one face multiplied by 2, or:
2(1 in x 20 in) = 40 in² (for the front face)
2(1 in x 22 in) = 44 in² (for the right face)
Therefore, the total surface area of the desktop is:
880 in² + 40 in² + 44 in² = 964 in²
Therefore, the surface area of the desktop is 964 square inches.
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An illustration shows three adjoining rectangular prisms placed together and labeled from the left as 2, 1, and 3. The length of the rectangular prisms along the front base is 20 inches for each. The depth of each adjoining prism is 20 inches. The height of the rectangular prism on the left labeled 2 is 11 inches; the height of the rectangular prism in the center labeled 1 is 15 inches; the height of the rectangular prism on the right labeled 3 is 7 inches.
At the Olympics, the winners of the gold, silver, and bronze medals stand on a tiered pedestal.
Assuming each pedestal is of equal width and depth, find the total surface area of the stand.
To find the total surface area of the stand, we need to find the surface area of each rectangular prism and add them up.
The three adjoining rectangular prisms form a stepped structure that resembles a staircase or a tiered pedestal. To calculate the surface area, we need to break down the structure into its individual rectangular prisms.
Starting from the bottom, we have:
- Rectangular prism 2: 20 in x 20 in x 11 in
- Rectangular prism 1: 20 in x 20 in x 15 in
- Rectangular prism 3: 20 in x 20 in x 7 in
We can find the surface area of each rectangular prism by calculating the area of each face and adding them up:
- For rectangular prisms 2 and 3:
- Front and back faces: 20 in x 11 in = 220 in² (each)
- Top and bottom faces: 20 in x 20 in = 400 in² (each)
- Left and right faces: 11 in x 20 in = 220 in² (for prism 2); 7 in x 20 in = 140 in² (for prism 3)
- For rectangular prism 1:
- Front and back faces: 20 in x 15 in = 300 in² (each)
- Top and bottom faces: 20 in x 20 in = 400 in² (each)
- Left and right faces: 15 in x 20 in = 300 in²
Now we can add up the surface areas of all three rectangular prisms:
- 2 x (220 + 400 + 220) = 1,680 in²
- 2 x (300 + 400 + 300) = 2,000 in²
- 2 x (220 + 400 + 140) = 1,520 in²
Therefore, the total surface area of the stand is:
1,680 in² + 2,000 in² + 1,520 in² = 5,200 in²
Therefore, the total surface area of the stand is 5,200 square inches.
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A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side is 3 feet. Corners are marked with right angles.
Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?
1$$ feet
We can find the width of the closet by subtracting the width of the removed rectangular area from the original width, which gives us a width of 7 feet (10 feet - 8 feet - unknown width = 2 feet, so the unknown width = 1 foot).
The area of the closet is given as 36 square feet. Since the closet is rectangle-shaped, we can use the formula for the area of a rectangle: area = length x width. We know the width is 7 feet, so we can solve for the length:
36 sq ft = length x