10 cm 10cm 10cm 6cm 8cm solve for the surface area of the triangle prism
To find the surface area of a triangular prism, you need to calculate the area of each of the faces and add them together.
1. The triangular base has sides of 10 cm, 10 cm, and 6 cm. To find the area of the base triangle, you can use Heron's formula:
s = (10 + 10 + 6) / 2 = 13 cm
Area = √(13(13-10)(13-10)(13-6)) = √(13*3*3*7) = √(819) ≈ 28.64 cm²
2. The triangular base has one of its sides as the height of the prism, which is 8 cm. So, the area of the two triangular bases would be 2 * 28.64 ≈ 57.28 cm².
3. The lateral faces of the prism are rectangles with a length of 10 cm and a width of 8 cm. There are 3 lateral faces, so the total area of the lateral faces is 3 * 10 * 8 = 240 cm².
Therefore, the total surface area of the triangular prism is the sum of the base areas and the lateral areas:
57.28 + 240 = 297.28 cm²
So, the surface area of the triangular prism is 297.28 cm².