A triangular, prism and its dimensions in centimeters are shown the graph
17cm 15cm 8cm 10cm
What is the total surface area of the prism in square centimeters
720 cm²
600 cm²
460 cm²
520 cm²
Total surface area of a triangular prism can be calculated by adding the areas of its three faces.
The formula for the total surface area of a triangular prism is:
Total Surface Area = 2 * (Base Area) + (Lateral Surface Area).
Given that the base of the triangular prism is a triangle with dimensions 10cm, 8cm and 17cm.
Base Area = 1/2 * base * height
Base Area = 1/2 * 10cm * 8cm = 40 cm²
Next, calculate the lateral surface area of the prism:
Lateral Surface Area = Perimeter of base * height = (10 + 8 + 17) * 15 = 375 cm²
Now, calculate the total surface area:
Total Surface Area = 2 * (40) + 375
Total Surface Area = 80 + 375
Total Surface Area = 455 cm²
Therefore, the total surface area of the prism is 455 cm². None of the given options match this, so the closest option is 460 cm².