If x = 9 units, Y = 14 units, Z = 16 units, and h = 6 units, what is the surface area of the triangular prism shown above?
A. 680 square units
B. 516 square units
C. 672 square units
D. 596 square units
To find the surface area of the triangular prism, we need to calculate the area of all five faces (two congruent triangles and three rectangles).
The area of a triangle is given by the formula: 1/2 * base * height.
The area of a rectangle is given by the formula: length * width.
1. Area of the two triangle faces:
For the triangle with base x = 9 units and height h = 6 units:
Area = 1/2 * 9 * 6 = 27 square units
Since there are two congruent triangles, the total area for both triangles is 2 * 27 = 54 square units.
2. Area of the three rectangular faces:
- For the rectangle with dimensions x and h:
Area = 9 * 6 = 54 square units
- For the rectangle with dimensions y and h:
Area = 14 * 6 = 84 square units
- For the rectangle with dimensions y and z:
Area = 14 * 16 = 224 square units
Now, add up the area of all faces to find the total surface area:
Total surface area = 54 (triangles) + 54 (rectangle 1) + 84 (rectangle 2) + 224 (rectangle 3) = 416 square units
Therefore, the total surface area of the triangular prism is 416 square units.
None of the options provided match the calculated surface area.