se the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is 9 centimeters. The width of the middle rectangle is 5 centimeters. Two right triangles adjoin the middle rectangle at the top and bottom. The perpendicular side measures 12 centimeters and the hypotenuse measures 13 centimeters.
Using the net, what is the surface area of the triangular prism?
(1 point)
cm2
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To find the surface area of the triangular prism, we need to find the area of each of the 5 faces and then add them together.
1. The two rectangular faces on the sides have an area of length x width. Since the length is 9 cm and the width is 5 cm, the area for each rectangular face is 9 cm x 5 cm = 45 cm2.
2. The two triangular faces on the top and bottom have an area of (1/2) x base x height. The base is 9 cm and the height is 12 cm, so the area for each triangular face is (1/2) x 9 cm x 12 cm = 54 cm2.
3. The middle rectangular face has an area of 5 cm x 9 cm = 45 cm2.
Now, add up the areas of all 5 faces:
2(45 cm2) (rectangular faces) + 2(54 cm2) (triangular faces) + 45 cm2 (middle face) = 90 cm2 + 108 cm2 + 45 cm2 = 243 cm2
Therefore, the surface area of the triangular prism is 243 cm2.
try again
To find the surface area of the triangular prism, we need to calculate the areas of all the individual faces and then add them together.
1. The two rectangular faces on the sides have a length of 9 cm and a width of 5 cm. The area of each rectangular face is 9 cm x 5 cm = 45 cm^2. Since there are two of these faces, the total area for these faces is 2 x 45 cm^2 = 90 cm^2.
2. The two triangular faces on the top and bottom are right triangles with a base of 9 cm and height of 12 cm. The area of each triangular face is (1/2) x base x height = (1/2) x 9 cm x 12 cm = 54 cm^2. Since there are two of these faces, the total area for these faces is 2 x 54 cm^2 = 108 cm^2.
3. The middle rectangular face has the same dimensions as the side faces, so it also has an area of 45 cm^2.
Now, add up the areas of all 5 faces:
90 cm^2 (side faces) + 108 cm^2 (top and bottom faces) + 45 cm^2 (middle face) = 243 cm^2
Therefore, the surface area of the triangular prism is 243 cm^2.