Find the total surface area of the triangular prism shown below.
Lateral Face:11
Base:6
Face1:5
Face2:5
To find the total surface area of the triangular prism, we need to calculate the area of the lateral faces and the two triangular bases.
1. Lateral faces:
The lateral faces are rectangles with the height equal to the height of the prism and the bases equal to the perimeter of the triangular bases. The perimeter of the triangle is:
Perimeter = 5 + 6 + 5 = 16
So the area of each lateral face is:
Area = height x perimeter = 11 x 16 = 176
Since there are two lateral faces, the total area of the lateral faces is:
Total lateral area = 2 x 176 = 352
2. Triangular base:
The area of a triangle is given by:
Area = 0.5 x base x height
For each triangular base:
Area = 0.5 x 6 x 11 = 33
Since there are two triangular bases, the total area of the bases is:
Total base area = 2 x 33 = 66
Now, the total surface area of the triangular prism is the sum of the lateral faces and the bases:
Total surface area = Total lateral area + Total base area
Total surface area = 352 + 66
Total surface area = 418
Therefore, the total surface area of the triangular prism shown is 418.