Surface Area of Triangular Prisms Quick Check
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Question
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
822 square meters
822 square meters
779 square meters
779 square meters
768 square meters
768 square meters
790 square meters
To find the surface area of the net of the triangular prism, we need to calculate the area of each individual face and then add them together.
1. Area of the triangular front face:
Area = 0.5 * base * height
Area = 0.5 * 16m * 15m
Area = 120 square meters
2. Area of the rectangular face:
Area = length * width
Area = 17m * 11m
Area = 187 square meters
3. Two triangular side faces:
To find the area of one triangle, we need to first calculate the hypotenuse using the Pythagorean theorem:
c = √(a^2 + b^2)
c = √(16^2 + 15^2)
c = √(256 + 225)
c = √481
c ≈ 21.93
Now we can calculate the area of one triangle:
Area = 0.5 * base * height
Area = 0.5 * 17m * 21.93m
Area = 185.955 square meters
Since there are two identical side faces, the total area for both is:
2 * 185.955 = 371.91 square meters
Adding all the areas together:
120 (front face) + 187 (rectangular face) + 371.91 (two side faces) = 678.91 square meters
Therefore, the surface area of the net of the triangular prism is 678.91 square meters.
None of the provided options match the calculated answer, so none of them are correct.
bro just chose its not that hard
In that case, the closest option to the calculated answer of 678.91 square meters would be:
790 square meters
However, please note that this is not the exact correct answer but the closest option provided.