Find the lateral surface area of the triangular prism solve this problem by determining the area of the shape net
To find the lateral surface area of a triangular prism, we need to first find the area of the net (the shape that when folded creates the prism).
The net of a triangular prism consists of two congruent triangles (the bases of the prism) and three rectangles (the lateral faces of the prism).
1. Calculate the area of the two triangles:
- The base of the triangles is the base of the prism, which is 4 units.
- The height of the triangles is the height of the prism, which is 3 units.
- The area of one triangle is (1/2) * base * height = (1/2) * 4 * 3 = 6 square units.
- Since there are two identical triangles, the total area of the triangles is 2 * 6 = 12 square units.
2. Calculate the area of the three rectangles:
- The length of the rectangles is the perimeter of the base of the prism, which is 3 + 4 + 3 + 4 = 14 units.
- The height of the rectangles is the height of the prism, which is 3 units.
- The area of one rectangle is length * height = 14 * 3 = 42 square units.
- Since there are three identical rectangles, the total area of the rectangles is 3 * 42 = 126 square units.
3. Add the areas of the triangles and rectangles to find the total lateral surface area of the prism:
Lateral Surface Area = Area of Triangles + Area of Rectangles
Lateral Surface Area = 12 + 126
Lateral Surface Area = 138 square units
Therefore, the lateral surface area of the triangular prism is 138 square units.