Use the net as an aid to compute the surface area of the triangular prism.
Responses
A 192
192 m 2
B 216
216 m 2
C 240
240 m 2
D 300
one angle is 4m, 6m, 12m, and 5m
To calculate the surface area of a triangular prism, we need to find the lateral surface area (area of the three rectangular faces) and the area of the two triangular faces.
First, let's find the lateral surface area. The formula for the lateral surface area of a triangular prism is:
Lateral Surface Area = perimeter of the base x height
The perimeter of the base triangle is 4m + 6m + 12m = 22m
The height of the prism is 5m
Lateral Surface Area = 22m x 5m = 110m^2
Next, let's find the area of the two triangular faces. The formula for the area of a triangle is:
Area = 1/2 x base x height
The base of the triangle is 6m and the height is 5m
Area = 1/2 x 6m x 5m = 15m^2
Since there are two triangular faces, the total area for both triangular faces is:
2 x 15m^2 = 30m^2
Therefore, the total surface area of the triangular prism is the sum of the lateral surface area and the area of the two triangular faces:
Total Surface Area = Lateral Surface Area + 2 x Area of Triangular Face
Total Surface Area = 110m^2 + 30m^2 = 140m^2
Therefore, none of the given options are correct. The correct surface area of the triangular prism is 140 m^2.