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

1 answer

Total surface area of a triangular prism can be calculated by finding the sum of the areas of all its faces.

The triangular base of the prism has dimensions 17cm, 15cm, and 8cm. To find the area of the triangular base, we can use Heron's formula:

s = (a + b + c) / 2 = (17 + 15 + 8) / 2 = 20 cm

Area of triangular base = √[20(20-17)(20-15)(20-8)] = √[20(3)(5)(12)] = √(3600) = 60 cm²

Now, the two lateral faces of the prism are rectangles with dimensions 10cm (height) and the perimeter of the triangular base (40cm). The area of each lateral face is:

Area of rectangular lateral face = base x height = 40 cm x 10 cm = 400 cm²

The two lateral faces have a combined area of 400 cm² + 400 cm² = 800 cm²

Therefore, the total surface area of the triangular prism is the sum of the areas of its base and two lateral faces:

Total surface area = 60 cm² + 800 cm² = 860 cm²

Therefore, the total surface area of the prism is 860 square centimeters.