Answer:
The triangular prism has two triangular bases and three rectangular lateral faces.
First, we need to find the area of each triangular base. Using the formula for the area of a triangle:
base x height / 2
We can calculate the area of one triangular base as:
(10 x 12) / 2 = 60 units²
Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:
10 x 14 = 140 units²
To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:
Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)
Total surface area = 2 x 60 units² + 3 x 140 units²
Total surface area = 120 units² + 420 units²
Total surface area = 540 units²
Therefore, the surface area of the triangular prism is 540 square units.