olve for the surface area of the triangular prism. (1 point) Responses 280 square centimeters 280 square centimeters 320 square centimeters 320 square centimeters 180 square centimeters 180 square centimeters 260 square centimeters
To calculate the surface area of a triangular prism, you need to find the sum of the areas of all the faces.
First, find the area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 10cm * 6cm = 30 square cm (for one base)
Since there are two bases, the total area for the bases is:
30 square cm * 2 = 60 square cm
Next, find the area of the three rectangular faces:
Area = length * width
Area = 10cm * 6cm = 60 square cm
Since there are three rectangular faces, the total area for the rectangular faces is:
60 square cm * 3 = 180 square cm
Finally, find the total surface area by adding up the areas of the bases and the rectangular faces:
Total Surface Area = 60 square cm + 180 square cm = 240 square cm
Therefore, the correct answer is not listed. The surface area of the triangular prism is 240 square centimeters.
not an option
Apologies for the miscalculation. Let's re-evaluate the surface area of the triangular prism:
1. Calculate the area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 10cm * 6cm = 30 square cm (for one base)
Since there are two bases, the total area for the bases is:
30 square cm * 2 = 60 square cm
2. Calculate the area of the three rectangular faces:
The two rectangles on the sides (10 cm by 3 cm):
Area = length * width
Area = 10cm * 3cm = 30 square cm (for one side rectangle)
There are 2 side rectangles, so total area for the side rectangles is:
30 square cm * 2 = 60 square cm
The rectangle on the top (6 cm by 3 cm):
Area = 6cm * 3cm = 18 square cm
Total area for the rectangular faces:
18 square cm + 60 square cm = 78 square cm
3. Add the areas of the triangular bases and the rectangular faces:
60 square cm (bases) + 78 square cm (rectangular faces) = 138 square cm
Therefore, the surface area of the triangular prism is 138 square centimeters. Since this option was not given, we can conclude that the closest option would be 180 square centimeters.