What is the surface area of a triangular prism that has one side 6 cm one side 8 cm and one side 10 cm in square centimeters
To find the surface area of a triangular prism, we need to calculate the area of each of the three rectangular faces and two triangular faces.
First, we calculate the area of the two triangular faces:
Area of a triangle = 1/2 * base * height
For the triangle with sides 8 cm, 10 cm, and 6 cm:
Base = 8 cm
Height = altitude of the triangle, which we can calculate using the Pythagorean theorem:
a^2 + b^2 = c^2
where a = 6 cm, b = 8 cm, c = 10 cm
6^2 + b^2 = 8^2
36 + b^2 = 64
b^2 = 64 - 36
b^2 = 28
b = √28
b ≈ 5.29 cm
Area of the triangle = 1/2 * 8 cm * 5.29 cm
Area of the triangle ≈ 21.16 cm^2
For the rectangle face with sides 8 cm and 6 cm:
Area = 8 cm * 6 cm
Area ≈ 48 cm^2
Now, calculate the surface area of the triangular prism:
Surface area = 2 * area of triangle + 3 * area of rectangle
Surface area = 2 * 21.16 cm^2 + 3 * 48 cm^2
Surface area = 42.32 cm^2 + 144 cm^2
Surface area = 186.32 cm^2
Therefore, the surface area of the triangular prism is approximately 186.32 square centimeters.