To solve for the surface area of the triangular prism, we need to find the area of each face and then add them together.
1. Area of the triangular base:
The base is a triangle with a base of 10 cm and a height of 6 cm.
Area = (1/2) * base * height
Area = (1/2) * 10 * 6
Area = 30 square cm
2. Area of the top triangular face:
Since the top face is congruent to the base, the area is also 30 square cm.
3. Area of the three rectangular faces:
There are three rectangular faces with dimensions:
- 10 cm by 6 cm
- 10 cm by 8 cm
- 6 cm by 8 cm
Calculating the area of each rectangular face:
1. 10 cm by 6 cm: 10 * 6 = 60 square cm
2. 10 cm by 8 cm: 10 * 8 = 80 square cm
3. 6 cm by 8 cm: 6 * 8 = 48 square cm
Total area of the three rectangular faces = 60 + 80 + 48 = 188 square cm
Finally, add up the areas of all the faces:
30 + 30 + 188 = 248 square cm
Therefore, the surface area of the triangular prism is 248 square centimeters.
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