If X = 8 units, Y = 12 units, Z = 17 units, and h = 5 units, what is the surface area of the triangular prism shown above?(2 points)
Responses
468 square units
468 square units
510 square units
510 square units
596 square units
596 square units
536 square units
To calculate the surface area of the triangular prism, we need to find the area of the three rectangular faces and the two triangular faces separately and then sum them up.
1. Area of the three rectangular faces:
- Two of the rectangular faces have dimensions of X by Y, so their areas are 2 * X * Y.
- One of the rectangular faces has dimensions of Y by Z, so its area is Y * Z.
2. Area of the two triangular faces:
- Each triangular face is a right triangle, and its area can be calculated using the formula: 0.5 * base * height.
- The base of each triangle is X, and the height is h.
Now we calculate the total surface area:
(2 * X * Y) + (Y * Z) + (2 * 0.5 * X * h) = (2 * 8 * 12) + (12 * 17) + (2 * 0.5 * 8 * 5) = 192 + 204 + 40 = 436 square units
Therefore, the surface area of the triangular prism is 436 square units.