To find the surface area of the triangular prism, we need to find the areas of each of the individual shapes that make up the net and then add them together.
1. Area of the two triangles:
- Each triangle has a base of 10 mm and a height of 9 mm, so the area of each triangle is (1/2) * base * height = (1/2) * 10 * 9 = 45 mm^2
- Since there are two triangles, the total area for the two triangles is 2 * 45 = 90 mm^2
2. Area of the three rectangles:
- Top rectangle: base = 10 mm and height = 40 mm, so area = 10 * 40 = 400 mm^2
- Left rectangle: base = 9 mm and height = 40 mm, so area = 9 * 40 = 360 mm^2
- Bottom rectangle: base = 10 mm and height = 41 mm, so area = 10 * 41 = 410 mm^2
- Total area for the three rectangles is 400 + 360 + 410 = 1170 mm^2
Adding the area of the two triangles and the three rectangles together we get:
90 (area of two triangles) + 1170 (area of three rectangles) = 1260 mm^2
Therefore, the surface area of the triangular prism is 1260 mm^2. The closest answer choice is 1,260 mm^2.
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
3 answers
are u absolutley sure
Let's double check the calculation:
1. Area of the two triangles: 90 mm^2
2. Area of the three rectangles: 1170 mm^2
Adding these together: 90 + 1170 = 1260 mm^2
Therefore, the surface area of the triangular prism is indeed 1260 mm^2. The correct answer is 1,260 mm^2.
1. Area of the two triangles: 90 mm^2
2. Area of the three rectangles: 1170 mm^2
Adding these together: 90 + 1170 = 1260 mm^2
Therefore, the surface area of the triangular prism is indeed 1260 mm^2. The correct answer is 1,260 mm^2.