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.
Surface Area of Triangular Prisms Practice
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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
3 answers
no
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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.
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.
1 answer