What is the surface area of a triangular prism that has one side 6 cm one side 10 cm and another side of 10 cm in square centimeters
To find the surface area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular faces.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(1/2 * base * height) + (perimeter of base * height)
Given that one side of the triangle is 6 cm, another side is 10 cm, and the third side is 10 cm, we can determine the height of the triangle using the Pythagorean theorem.
Let the height of the triangle be h.
Using the Pythagorean theorem, we have:
(6)^2 + h^2 = (10)^2
36 + h^2 = 100
h^2 = 100 - 36
h^2 = 64
h = 8 cm
Now we can calculate the surface area of the triangular prism.
Area of one triangular base = 1/2 * 6 cm * 8 cm = 24 cm^2
Area of the other triangular base = 1/2 * 10 cm * 8 cm = 40 cm^2
Perimeter of the base = 6 cm + 10 cm + 10 cm = 26 cm
Surface Area = 2(24 cm^2 + 40 cm^2) + 26 cm * 8 cm
Surface Area = 2(64 cm^2) + 208 cm^2
Surface Area = 128 cm^2 + 208 cm^2
Surface Area = 336 cm^2
Therefore, the surface area of the triangular prism is 336 square centimeters.