Use damage to answer the questions, Solve for the surface area of a triangle prism 6 cm one side 10 cm 8 cm 10 cm
To find the surface area of a triangular prism, we need to calculate the area of each face and then add them all together.
First, we find the area of the two triangular faces. The base of the triangle is 6 cm and the height can be found using the Pythagorean theorem:
Height = √(8^2 - 3^2) = √(64 - 9) = √55
Area of one triangular face = (1/2) * base * height = (1/2) * 6 * √55 = 3√55 cm^2
Area of both triangular faces = 2 * 3√55 = 6√55 cm^2
Next, we find the area of the three rectangular faces. Two faces have dimensions 6 cm x 10 cm and one face has dimensions 8 cm x 10 cm.
Area of the two rectangular faces = 2 * (6 * 10) = 120 cm^2
Area of the third rectangular face = 8 * 10 = 80 cm^2
Finally, we add all the areas together:
Surface area of triangular prism = Area of both triangular faces + Area of all rectangular faces
Surface area = 6√55 + 120 + 80 = 6√55 + 200 cm^2
Therefore, the surface area of the triangular prism is approximately 6√55 + 200 square cm.