If X = 7 units, Y = 6 units, Z = 16 units, and h = 6 units, what is the surface area of the triangular prism shown above?
To find the surface area of a triangular prism, we need to calculate the area of each of the five faces and sum them up.
1. The area of the two triangular bases:
Each triangular base has a base of X = 7 units and a height of h = 6 units. The formula to calculate the area of a triangle is A = 1/2 * base * height. So, the area of one triangular base is:
A1 = 1/2 * X * h
A1 = 1/2 * 7 * 6
A1 = 21 square units
The total area of both triangular bases is:
2 * A1 = 2 * 21 = 42 square units
2. The area of the three rectangular faces:
There are three rectangular faces in a triangular prism. The area of each rectangular face is the product of the two adjacent sides. The three rectangular faces have the following dimensions:
- Two faces have dimensions X * Y = 7 * 6 square units
- One face has dimensions Y * Z = 6 * 16 square units
Total area of the three rectangular faces:
2 * X * Y + Y * Z = 2 * 7 * 6 + 6 * 16 = 84 + 96 = 180 square units
Therefore, the total surface area of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces:
Total surface area = 42 + 180 = 222 square units
So, the surface area of the triangular prism is 222 square units.