what is the surface area of the triangular prism with the numbers 8,10,6,9
To find the surface area of a triangular prism, you need to calculate the area of the two triangular bases and the three rectangular sides.
First, we calculate the area of the two triangular bases:
Base 1:
Using the given numbers 8, 10, and 6, we can find the area of the first triangle using Heron's formula:
s = (a + b + c) / 2 = (8 + 10 + 6) / 2 = 24 / 2 = 12
Area = √(s(s-a)(s-b)(s-c)) = √(12(12-8)(12-10)(12-6)) = √(12 * 4 * 2 * 6) = √(576) = 24
Base 2:
The area of the second triangle will be the same as the area of the first triangle since the dimensions are the same for both triangles.
Now, we calculate the area of the three rectangular sides:
Side 1:
Area = base * height = 8 * 9 = 72
Side 2:
Area = base * height = 10 * 9 = 90
Side 3:
Area = base * height = 6 * 9 = 54
Finally, we calculate the total surface area by adding the areas of the two bases and the three sides:
Total Surface Area = 2(24) + 72 + 90 + 54 = 48 + 72 + 90 + 54 = 264
Therefore, the surface area of the triangular prism is 264 square units.