What is the surface area of the triangular prism 8cm, 6cm, 9cm, 10cm???
____ square centimeters
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2(Base Area) + (Perimeter of Base x Height)
Given that the base of the triangular prism is a triangle with sides of 8cm, 6cm, and 10cm, we can calculate the area of the base using Heron's formula.
First calculate the semiperimeter of the base:
s = (8 + 6 + 10) / 2 = 12
Now calculate the area of the base using Heron's formula:
Area = √[12(12 - 8)(12 - 6)(12 - 10)]
Area = √(12*4*6*2) = √(576) = 24
Now calculate the perimeter of the base:
Perimeter = 8 + 6 + 10 = 24
Now calculate the total surface area:
Surface Area = 2(24) + (24 * 9)
Surface Area = 48 + 216
Surface Area = 264 square centimeters
Therefore, the surface area of the triangular prism is 264 square centimeters.