Use 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 horizontal rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the 3 rectangles is 1 centimeter. The length of the outer rectangles is 2.5 centimeters. The length of the middle rectangle is 3 centimeters. Two right triangles adjoin the middle rectangle on the top and bottom along the 3 centimeter side, with their perpendicular height measuring 2 centimeters. A right angle is shown where the perpendicular height intersects with the triangle base.
What is the surface area of the triangular prism whose net is shown?
A:6 cm2
B:2.48 cm2
C:8 cm2
D:14 cm2
To find the surface area of the triangular prism, we need to add up the areas of all the faces. We can start by finding the area of the three rectangles. The area of each rectangle is length times width:
- Area of outer rectangles = 2.5 cm x 1 cm x 2 = 5 cm2 (since there are two identical rectangles)
- Area of middle rectangle = 3 cm x 1 cm = 3 cm2
Next, we need to find the area of the two triangles. The area of a triangle is 1/2 times base times height:
- Area of top triangle = 1/2 x 3 cm x 2 cm = 3 cm2
- Area of bottom triangle = 1/2 x 3 cm x 2 cm = 3 cm2
Finally, we can add up the areas of all the faces to get the surface area of the prism:
5 cm2 + 5 cm2 + 3 cm2 + 3 cm2 + 3 cm2 = 19 cm2
However, we need to remember that the net shows all the faces of the prism, including the inside faces that we can't see. So we need to subtract the areas of the rectangles that form the inside faces. Since the inside faces are identical to the outer faces, each inside rectangle has an area of 5 cm2. There are two inside rectangles, so their combined area is 10 cm2. Subtracting this from the total surface area gives:
19 cm2 - 10 cm2 = 9 cm2
Therefore, the answer is not one of the options given.
Use 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 horizontal rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the 3 rectangles is 1 centimeter. The length of the outer rectangles is 2.5 centimeters. The length of the middle rectangle is 3 centimeters. Two right triangles adjoin the middle rectangle on the top and bottom along the 3 centimeter side, with their perpendicular height measuring 2 centimeters. A right angle is shown where the perpendicular height intersects with the triangle base.
What is the surface area of the triangular prism whose net is shown?
A:6 cm2
B:2.48 cm2
C:8 cm2
D:14 cm2
To find the surface area of the triangular prism, we need to add up the areas of all the faces. We can start by finding the area of the three rectangles. The area of each rectangle is length times width:
- Area of outer rectangles = 2.5 cm x 1 cm x 2 = 5 cm2 (since there are two identical rectangles)
- Area of middle rectangle = 3 cm x 1 cm = 3 cm2
Next, we need to find the area of the two triangles. The area of a triangle is 1/2 times base times height:
- Area of top triangle = 1/2 x 3 cm x 2 cm = 3 cm2
- Area of bottom triangle = 1/2 x 3 cm x 2 cm = 3 cm2
Finally, we can add up the areas of all the faces to get the surface area of the prism:
5 cm2 + 5 cm2 + 3 cm2 + 3 cm2 + 3 cm2 = 19 cm2
However, we need to remember that the net shows all the faces of the prism, including the inside faces that we can't see. So we need to subtract the areas of the rectangles that form the inside faces. Since the inside faces are identical to the outer faces, each inside rectangle has an area of 5 cm2. There are two inside rectangles, so their combined area is 10 cm2. Subtracting this from the total surface area gives:
19 cm2 - 10 cm2 = 9 cm2
Therefore, the answer is not one of the options given.
To find the surface area of the triangular prism, we need to calculate the area of each of the individual surfaces and then add them together.
Surface 1: The top and bottom rectangles have dimensions of 1 cm by 2.5 cm. So the area of each of these rectangles is 1 cm * 2.5 cm = 2.5 cm². Since there are two identical rectangles, the total area of the top and bottom is 2 * 2.5 cm² = 5 cm².
Surface 2: The middle rectangle has dimensions of 1 cm by 3 cm. So the area of this rectangle is 1 cm * 3 cm = 3 cm².
Surface 3: The two right triangles have a base of 3 cm and a height of 2 cm. The area of each triangle is 1/2 * base * height = 1/2 * 3 cm * 2 cm = 3 cm². Since there are two identical triangles, the total area of the two triangles is 2 * 3 cm² = 6 cm².
Now let's add up the areas of all the surfaces:
Surface 1 + Surface 2 + Surface 3 = 5 cm² + 3 cm² + 6 cm² = 14 cm².
Therefore, the surface area of the triangular prism is 14 cm².
So, the correct option is D: 14 cm².