find the area of the triangular prism
the numbers are 14 in 12 in 5 in 13 in
To find the area of a triangular prism, you need to calculate the total surface area of all the faces of the prism.
First, let's find the area of the two triangular bases:
1. Find the area of the base triangle:
A = 1/2 * (12 in) * (5 in) = 30 square inches
2. Since there are two triangular bases, the total area of the bases is 2 * 30 = 60 square inches
Next, find the lateral surface area of the prism (the three rectangular faces):
1. Find the area of each rectangular face:
- Face 1: (14 in) * (12 in) = 168 square inches
- Face 2: (14 in) * (12 in) = 168 square inches
- Face 3: (13 in) * (12 in) = 156 square inches
2. Add up the areas of the rectangular faces: 168 + 168 + 156 = 492 square inches
Finally, find the total surface area of the triangular prism by adding the area of the bases and the lateral surface area:
Total surface area = area of bases + lateral surface area
Total surface area = 60 + 492
Total surface area = 552 square inches
Therefore, the area of the triangular prism is 552 square inches.