Question

what is the total surface are of the traingular prism in cm, if the base is 12, the height is 4, the length is 18, and the diagonal length is 13?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the triangular prism, we need to calculate the lateral surface area and the two triangular base areas.

The lateral surface area of a triangular prism is given by the formula:

Lateral surface area = perimeter of base x height of prism

The perimeter of the base of the triangular prism is the sum of the three sides of the base triangle:

Perimeter of base = 12 + 12 + 18 = 42 cm

So, the lateral surface area of the triangular prism is:

Lateral surface area = 42 cm x 4 cm = 168 cm²

The area of each triangular base can be found using the formula:

Area of triangle = 1/2 x base x height

Therefore, the area of each triangular base is:

Area of triangle = 1/2 x 12 cm x 4 cm = 24 cm²

Now, we can find the total surface area of the triangular prism by adding the lateral surface area and the two triangular base areas:

Total surface area = Lateral surface area + 2 x Area of triangle
Total surface area = 168 cm² + 2 x 24 cm²
Total surface area = 168 cm² + 48 cm²
Total surface area = 216 cm²

Therefore, the total surface area of the triangular prism is 216 cm².