10 cm 8 cm 9 cm 6 cm
What is the surface area of the triangle prism
To calculate the surface area of a triangular prism, we need to find the areas of the two triangular bases and the three rectangular sides, and then add them together.
Given that the base of the prism is a triangle with sides of 10 cm, 8 cm, and 9 cm, we can use Heron's formula to find the area of the base triangle:
S = (a + b + c) / 2 = (10 + 8 + 9) / 2 = 13.5
Area = √(s(s-a)(s-b)(s-c)) = √(13.5(3.5)(5.5)(4.5)) = √(894.75) ≈ 29.92 cm^2
Now, we need to calculate the three rectangular sides. Two of the sides will be the same as the base triangle's area, and the third side will be the rectangle's area:
1. Area of the first side = 10 cm x 6 cm = 60 cm^2
2. Area of the second side = 8 cm x 6 cm = 48 cm^2
3. Area of the third side = 9 cm x 6 cm = 54 cm^2
Now, sum up all the areas:
Total surface area = 2(base triangle area) + 3(rectangular side areas)
Total surface area = 2(29.92 cm^2) + 3(60 cm^2 + 48 cm^2 + 54 cm^2)
Total surface area = 59.84 cm^2 + 450 cm^2
Total surface area ≈ 509.84 cm^2
Therefore, the surface area of the triangular prism is approximately 509.84 cm^2.