To calculate the surface area of the triangular prism, we need to find the area of each of the individual surfaces and then add them all up.
1. The area of the square base: (12m x 12m) = 144m^2
2. The area of the triangular sides: There are 3 triangular sides on a triangular prism. To find the area of one of the triangular sides, we can use the formula for the area of a triangle, which is 1/2 * base * height.
For the triangular sides with base 12m and height 8m: 1/2 * 12m * 8m = 48m^2
For the triangular sides with base 10m and height 8m: 1/2 * 10m * 8m = 40m^2
3. The area of the rectangular sides: There are 3 rectangular sides on a triangular prism. To find the area of one of the rectangular sides, we can use the formula for the area of a rectangle, which is length * width.
For the rectangular sides with length 12m and width 10m: 12m * 10m = 120m^2
Adding all the areas together:
Square base: 144m^2
Triangular sides: 48m^2 + 48m^2 + 40m^2 = 136m^2
Rectangular sides: 120m^2 + 120m^2 + 120m^2 = 360m^2
Total surface area of the triangular prism: 144m^2 + 136m^2 + 360m^2 = 640m^2
Therefore, the surface area of the triangular prism is 640 square meters.
a net of a triangular prism is shown below.
What is the surface area, in square meters, of the triangular prism.
12m is the length of the square, 12m is the middle of the square, 8m is the middle of the triangle, 10m is the length of the triangle, 10m is the width of the square
1 answer