Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
(1 point)
Responses
779 square meters
779 square meters
822 square meters
822 square meters
790 square
meters
779 square meters
779 square meters
822 square meters
822 square meters
790 square meters
790 square meters
768 square meters
768 square meters
To find the surface area of the net of the triangular prism, we need to calculate the area of each individual face (front triangular face, right rectangular face, and the two side faces) and then add them up.
Front triangular face: Area = (1/2) * base * height = (1/2) * 16 * 15 = 120 square meters
Right rectangular face: Area = length * width = 17 * 11 = 187 square meters
Side faces (assumed to be right triangles with hypotenuse as 17 meters and one leg as 15 meters, so using Pythagorean theorem, the other leg is √(17^2 - 15^2) = 8 meters): Area = (1/2) * base * height = (1/2) * 8 * 17 = 68 square meters for each side face
Total surface area = Front triangular face + Right rectangular face + 2 * Side faces
Total surface area = 120 + 187 + 2*68 = 120 + 187 + 136 = 443 + 136 = 579 square meters
Therefore, the correct answer is not provided among the options. The correct surface area of the net of the triangular prism is 579 square meters.