Use the image to answer the question.
The net appears as three horizontal rectangles joined one on top of the other. The top, left, and bottom sides of the middle rectangle are drawn with dashed lines. The height of the middle rectangle is 40 millimeters. The width of the middle rectangle is 10 millimeters. The middle rectangle has a right triangle adjoining its left side. The top horizontal side of the triangle is 9 millimeters. The right side of the bottom rectangle is dashed and is 41 millimeters. An unmarked triangle the same size and shape as the other triangle adjoins the right side of the bottom rectangle. Its hypotenuse shares a side with the right side of the bottom rectangle.
The net of a triangular prism is shown. What is the surface area of the triangular prism?
(1 point)
To find the surface area of the triangular prism, we need to calculate the areas of each of the shapes that make up the prism.
1. The top and bottom rectangles: 2 rectangles, each with dimensions 10mm x 41mm.
Area = 2(10mm x 41mm) = 820 square millimeters
2. The front and back triangles: 2 triangles, each with base 9mm and height 40mm.
Area = 2(1/2 x 9mm x 40mm) = 360 square millimeters
3. The lateral surface area: this is the combined area of the three outer rectangles.
First rectangle: 10mm x 40mm = 400 square millimeters
Second rectangle: 10mm x 41mm = 410 square millimeters
Third rectangle: 41mm x 40mm = 1640 square millimeters
Total lateral surface area = 400 + 410 + 1640 = 2450 square millimeters
Now, add up the areas of all the shapes to find the total surface area of the triangular prism.
Total surface area = 820 + 360 + 2450 = 3630 square millimeters
Therefore, the surface area of the triangular prism is 3630 square millimeters.
nope it is in the one thousands
I apologize for the error in my previous response. Let's recalculate the surface area of the triangular prism.
1. Top and bottom rectangles: 2 rectangles, each with dimensions 10mm x 41mm.
Area = 2(10mm x 41mm) = 820 square millimeters
2. Front and back triangles: 2 triangles, each with base 9mm and height 40mm.
Area = 2(1/2 x 9mm x 40mm) = 360 square millimeters
3. Lateral surface area: the combined area of the three outer rectangles.
First rectangle: 10mm x 40mm = 400 square millimeters
Second rectangle: 41mm x 40mm = 1640 square millimeters
Total lateral surface area = 2(400mm + 1640mm) = 2080 square millimeters
Now, add up the areas of all the shapes to find the total surface area of the triangular prism.
Total surface area = Top and bottom rectangles + Front and back triangles + Lateral surface area
Total surface area = 820 + 360 + 2080 = 3260 square millimeters
Therefore, the correct surface area of the triangular prism is 3260 square millimeters.
Use the image to answer the question.
The net appears as three horizontal rectangles joined one on top of the other. The top, left, and bottom sides of the middle rectangle are drawn with dashed lines. The height of the middle rectangle is 40 millimeters. The width of the middle rectangle is 10 millimeters. The middle rectangle has a right triangle adjoining its left side. The top horizontal side of the triangle is 9 millimeters. The right side of the bottom rectangle is dashed and is 41 millimeters. An unmarked triangle the same size and shape as the other triangle adjoins the right side of the bottom rectangle. Its hypotenuse shares a side with the right side of the bottom rectangle.
The net of a triangular prism is shown. What is the surface area of the triangular prism?
(1 point)
Responses
1,080 mm.2
1,080 mm.2
1,620 mm.2
1,620 mm.2
1,220 mm.2
1,220 mm.2
1,260 mm.2
1,260 mm.2
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To find the surface area of the triangular prism, we need to calculate the areas of each of the shapes that make up the prism.
1. Top and bottom rectangles: 2 rectangles, each with dimensions 10mm x 41mm.
Area = 2(10mm x 41mm) = 820 square millimeters
2. Front and back triangles: 2 triangles, each with base 9mm and height 40mm.
Area = 2(1/2 x 9mm x 40mm) = 360 square millimeters
3. Lateral surface area: this is the combined area of the three outer rectangles.
First rectangle: 10mm x 40mm = 400 square millimeters
Second rectangle: 10mm x 40mm = 400 square millimeters
Third rectangle: 41mm x 40mm = 1640 square millimeters
Total lateral surface area = 400 + 400 + 1640 = 2440 square millimeters
Now, add up the areas of all the shapes to find the total surface area of the triangular prism.
Total surface area = Top and bottom rectangles + Front and back triangles + Lateral surface area
Total surface area = 820 + 360 + 2440 = 3620 square millimeters
Therefore, the surface area of the triangular prism is 3,620 square millimeters.
So, the option closest to the calculated answer is:
1,220 mm.2