what is the surface area of a triangular prism with a height of 8 cm length of 10 cm and width of 16 cm and a hypotenuse of 12.81 cm
532.96 cm²
572.96 cm²
528 cm²
604.96 cm²
To find the surface area of a triangular prism, you need to find the area of the two triangular bases, as well as the three rectangular faces.
First, find the area of the two triangular bases:
Area of a triangle = 1/2 * base * height
Base = 10 cm
Height = 8 cm
Area of one triangle = 1/2 * 10 * 8 = 40 cm²
Area of both triangles = 2 * 40 cm² = 80 cm²
Next, find the area of the three rectangular faces:
Rectangle 1:
Length = 10 cm
Width = 8 cm
Area = length * width = 10 * 8 = 80 cm²
Rectangle 2:
Length = 16 cm
Width = 8 cm
Area = length * width = 16 * 8 = 128 cm²
Rectangle 3:
Length = 16 cm
Width = 10 cm
Area = length * width = 16 * 10 = 160 cm²
Total area of rectangular faces = 80 + 128 + 160 = 368 cm²
Now, add the areas of the two triangles and three rectangles to find the total surface area of the triangular prism:
80 cm² (triangular bases) + 368 cm² (rectangular faces) = 448 cm²
Therefore, the correct answer is not listed in the given options. The closest option is 528 cm², but it does not match the calculated surface area.