Question
Use the image to answer the question.
An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.
What is the surface area of the net of the triangular prism?
(1 point)
To find the surface area of the net of the triangular prism, we need to calculate the area of each individual shape and then add them together.
1. Area of the top rectangle:
Length = 10 cm, Width = 5 cm
Area = Length x Width = 10 cm x 5 cm = 50 cm²
2. Area of the bottom rectangle:
Length = 10 cm, Width = 5 cm
Area = Length x Width = 10 cm x 5 cm = 50 cm²
3. Area of the middle rectangle:
Length = 5 cm, Width = 4 cm (height of the triangle)
Area = Length x Width = 5 cm x 4 cm = 20 cm²
4. Area of one of the triangles:
Base = 5 cm, Height = 4 cm
Area = 0.5 x Base x Height = 0.5 x 5 cm x 4 cm = 10 cm²
Since there are two identical triangles, the total area for both triangles would be 10 cm² x 2 = 20 cm²
Adding all the areas together:
Total Surface Area = 50 cm² (top rectangle) + 50 cm² (bottom rectangle) + 20 cm² (middle rectangle) + 20 cm² (both triangles) = 140 cm²
Therefore, the surface area of the net of the triangular prism is 140 square centimeters.
incorrect.
I apologize for the mistake.
Let's calculate the surface area of the net of the triangular prism again:
1. Area of the top rectangle:
Length = 10 cm, Width = 5 cm
Area = Length x Width = 10 cm x 5 cm = 50 cm²
2. Area of the bottom rectangle:
Length = 10 cm, Width = 5 cm
Area = Length x Width = 10 cm x 5 cm = 50 cm²
3. Area of the middle rectangle:
Length = 5 cm (base of the triangle), Width = 5 cm (shared with the top and bottom rectangles)
Area = Length x Width = 5 cm x 5 cm = 25 cm²
4. Area of one of the triangles:
Base = 5 cm, Height = 4 cm
Area = 0.5 x Base x Height = 0.5 x 5 cm x 4 cm = 10 cm²
Since there are two identical triangles, the total area for both triangles would be 10 cm² x 2 = 20 cm²
Adding all the areas together:
Total Surface Area = 50 cm² (top rectangle) + 50 cm² (bottom rectangle) + 25 cm² (middle rectangle) + 20 cm² (both triangles) = 145 cm²
Therefore, the surface area of the net of the triangular prism is 145 square centimeters.