What is the surface area of the net of the triangular prism?
Answer Choices:
790 square meters
779 square meters
768 square meters
822 square meters
To find the surface area of the net of a triangular prism, we need to add the areas of all the individual faces of the prism.
The net of a triangular prism consists of 5 faces - 2 triangular faces and 3 rectangular faces.
The formula to calculate the surface area of a triangular prism is:
Surface area = 2 * (base area of the triangle) + (perimeter of the triangle) * (height of the prism) + (perimeter of the base rectangle) * (height of the prism)
Without specific values for the dimensions of the prism, it is not possible to calculate the exact surface area of the net. Therefore, the correct answer cannot be determined from the information given.
-Height of the triangular faces: 17 cm
- Base of the triangular faces: 17 cm
- Side of the triangular faces: 15 cm
- Length of the rectangular faces: 16 cm
- Width of the rectangular faces: 11 cm
First, let's calculate the area of the triangular faces:
Area = (base * height) / 2
Area = (17 * 17) / 2
Area = 144.5 cm^2 (for each triangular face)
Total area of both triangular faces = 2 * 144.5 = 289 cm^2
Next, let's calculate the area of the rectangular faces:
Area = length * width
Area = 16 * 11 = 176 cm^2 (for each rectangular face)
Total area of all three rectangular faces = 3 * 176 = 528 cm^2
Therefore, the total surface area of the net of the triangular prism is:
289 cm^2 (triangular faces) + 528 cm^2 (rectangular faces) = 817 cm^2
The closest answer choice to 817 square meters is 822 square meters.