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 find the surface area of the triangular prism, we first need to find the areas of the two triangular bases and the three rectangular faces.
1. Area of one triangular base:
Area = (1/2) * base * height
Area = (1/2) * X * h
Area = (1/2) * 8 * 5
Area = 20 square units
2. Total area of both triangular bases:
Total base area = 2 * Area
Total base area = 2 * 20
Total base area = 40 square units
3. Area of three rectangular faces:
- Opposite sides are equal in a prism, so we can calculate the areas of two rectangles and then double it.
a. Rectangle with sides X and Y:
Area = X * Y
Area = 8 * 12
Area = 96 square units
b. Rectangle with sides Y and Z:
Area = Y * Z
Area = 12 * 17
Area = 204 square units
Total area of three rectangular faces = 2 * (96 + 204)
Total area of three rectangular faces = 2 * 300
Total area of three rectangular faces = 600 square units
4. Total surface area of the triangular prism:
Surface area = Total base area + Total area of three rectangular faces
Surface area = 40 + 600
Surface area = 640 square units
Therefore, the surface area of the triangular prism is 640 square units. None of the provided options match this calculation.