What is the surface area of a triangular prism that has one side 6 cm one side 10 cm one side 8 cm and another side 10 cm in square centimeters
To calculate the surface area of a triangular prism, we need to find the areas of the two triangular bases and the three rectangular faces.
First, let's find the area of one of the triangular bases:
Using Heron's formula, we can calculate the area of a triangle with sides 6 cm, 8 cm, and 10 cm:
s = (6 + 8 + 10) / 2 = 12
Area of triangle = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √(576) = 24 cm²
Since there are two triangular bases, the total area of the triangular bases is 2 * 24 = 48 cm².
Next, let's find the areas of the three rectangular faces:
The first face has dimensions of 6 cm x 10 cm = 60 cm²
The second face has dimensions of 8 cm x 10 cm = 80 cm²
The third face has dimensions of 6 cm x 8 cm = 48 cm²
The total area of the rectangular faces is 60 + 80 + 48 = 188 cm².
Finally, the total surface area of the triangular prism is the sum of the areas of the triangular bases and the three rectangular faces:
Total surface area = 48 + 188 = 236 cm²
Therefore, the surface area of the triangular prism is 236 square centimeters.