Question

What is the surface area, in square centimeters, of the triangular prism?

Answer 1

15 9 12 6 15 12

Answer 2

In order to answer this question, the measurements of the triangular prism, such as the length, width, and height, are required. Could you please provide these values?

Answer 3

To find the surface area of a triangular prism, we need to calculate the areas of each of the faces and then sum them up.

The triangular prism has a triangle base with dimensions 15 cm, 9 cm, and 12 cm. Let's calculate the area of the triangular base first using Heron's formula:

s = (15 + 9 + 12)/2 = 36/2 = 18

Area of the base triangle = √(18(18-15)(18-9)(18-12)) = √(18*3*9*6) = √2916 = 54 cm²

Now, let's calculate the areas of the rectangular faces:

Area of the rectangular face = length * width
Face 1: 15 cm * 9 cm = 135 cm²
Face 2: 6 cm * 15 cm = 90 cm²
Face 3: 15 cm * 12 cm = 180 cm²

Now, let's sum up all the areas:

Total surface area = 2 * (Area of the triangular base) + 3 * (Area of the rectangular faces)
= 2 * 54 cm² + 3 * (135 cm² + 90 cm² + 180 cm²)
= 108 cm² + 3 * 405 cm²
= 108 cm² + 1215 cm²
= 1323 cm²

Therefore, the surface area of the triangular prism is 1323 square centimeters.