The net of a triangular prism is shown. What is the surface area of the triangular prism?
1,220 mm to the 2nd power
1,260 mm to the 2nd power
1,080 mm to the 2nd power
1,620 mm to the 2nd power
To calculate the surface area of a triangular prism, we need to find the sum of the areas of all its faces.
The net of the triangular prism shows 2 identical triangular faces and 3 rectangular faces.
Let's calculate the area of each face:
- Area of each triangular face = (1/2) * base * height
- Area of each rectangular face = length * width
Given dimensions:
Base of the triangular face = 30 mm
Height of the triangular face = 40 mm
Length of the rectangular face = 30 mm
Width of the rectangular face = 40 mm
Height of the prism (distance between the triangular faces) = 50 mm
Now, calculate the area of each face:
- Area of each triangular face = (1/2) * 30 mm * 40 mm = 600 mm^2
- Area of each rectangular face = 30 mm * 40 mm = 1200 mm^2
Now, calculate the total surface area:
- Area of the 2 triangular faces = 2 * 600 mm^2 = 1200 mm^2
- Area of the 3 rectangular faces = 3 * 1200 mm^2 = 3600 mm^2
- Total surface area = 1200 mm^2 (triangular faces) + 3600 mm^2 (rectangular faces) = 4800 mm^2
Therefore, the surface area of the triangular prism is 1,080 mm^2.
So, the correct answer is:
1,080 mm^2