Surface Area of Triangular Prisms Practice
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Question
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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 width of the rectangles is 6 centimeters. The length of the middle rectangle is 8 centimeters. Two identical triangles adjoin the middle rectangle at the top and bottom with sides each measuring 8 centimeters and the perpendicular height measuring 6.9 centimeters.
What is the surface area of the triangular prism? Round the answer to the nearest tenth.
(1 point)
cm2
The surface area of the triangular prism can be calculated by finding the surface area of each individual shape and adding them up.
- Surface area of the middle rectangle: 8 cm (length) x 6 cm (width) = 48 cm^2
- Surface area of the two identical triangles: 2 x (1/2 x base x height) = 2 x (1/2 x 8 cm x 6.9 cm) = 2 x (4 cm x 6.9 cm) = 2 x 27.6 cm^2 = 55.2 cm^2
- Surface area of the lateral faces: 2 x (length x height) = 2 x (8 cm x 6.9 cm) = 2 x 55.2 cm^2 = 110.4 cm^2
Adding all the surface areas together:
48 cm^2 (middle rectangle) + 55.2 cm^2 (triangles) + 110.4 cm^2 (lateral faces) = 213.6 cm^2
Therefore, the surface area of the triangular prism is 213.6 cm^2.
no
I apologize for the mistake. Let's try again.
The surface area of a triangular prism can be calculated by finding the areas of all its faces and adding them together.
1. Area of the two triangular bases:
Area = 2 * (1/2 * base * height) = 2 * (1/2 * 8 cm * 6.9 cm) = 2 * (4 cm * 6.9 cm) = 55.2 cm^2
2. Area of the three rectangular faces:
- Front and back faces: 8 cm * 6.9 cm = 55.2 cm^2
- Two side faces: 6 cm * 6.9 cm = 41.4 cm^2
Total rectangular face area = 55.2 cm^2 + 55.2 cm^2 + 41.4 cm^2 = 151.8 cm^2
Adding the areas of the triangular bases and rectangular faces together:
55.2 cm^2 (triangular bases) + 151.8 cm^2 (rectangular faces) = 207 cm^2
Therefore, the surface area of the triangular prism is 207 cm^2. Thank you for your patience.