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
1,620 mm.2
1,620 mm.2
1,260 mm.2
1,260 mm.2
1,220 mm.2
1,220 mm.2
1,080 mm.2
1,080 mm.2
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The total surface area of a triangular prism is calculated by adding the area of the two triangular bases and the three rectangular faces.
The area of the triangular bases can be calculated using the formula: 1/2 * base * height.
For the top triangle: 1/2 * 10 mm * 40 mm = 200 mm^2
For the bottom triangle: 1/2 * 9 mm * 41 mm = 184.5 mm^2
The area of the three rectangular faces can be calculated by multiplying the length by the width.
For the middle rectangle: 10 mm * 40 mm = 400 mm^2
For the top rectangle: 9 mm * 40 mm = 360 mm^2
For the bottom rectangle: 9 mm * 41 mm = 369 mm^2
Adding all the areas together: 200 mm^2 + 184.5 mm^2 + 400 mm^2 + 360 mm^2 + 369 mm^2 = 1,513.5 mm^2
Therefore, the surface area of the triangular prism is closest to 1,520 mm^2.
wrong try again
To calculate the surface area of the triangular prism, we need to find the areas of each face and then sum them up.
- Area of the two triangular bases:
Area = 1/2 * base * height
Top base area = 1/2 * 10 mm * 40 mm = 200 mm^2
Bottom base area = 1/2 * 9 mm * 41 mm = 184.5 mm^2
- Area of the three rectangular faces:
Middle rectangle area = 10 mm * 40 mm = 400 mm^2
Top rectangle area = 9 mm * 40 mm = 360 mm^2
Bottom rectangle area = 9 mm * 41 mm = 369 mm^2
Now, summing up all the areas:
Total surface area = 2*(200 mm^2 + 184.5 mm^2) + 400 mm^2 + 360 mm^2 + 369 mm^2
Total surface area = 2*(384.5 mm^2) + 400 mm^2 + 360 mm^2 + 369 mm^2
Total surface area = 769 mm^2 + 400 mm^2 + 360 mm^2 + 369 mm^2
Total surface area = 1898 mm^2
Therefore, the surface area of the triangular prism is 1898 mm^2.