If x =8 units Y =12 units. z =17 units and h =5 units. what is the surface area of the 3d triangular prism shown above? (2 points)
468 square units
510 square units
596 square units
536 square units
To find the surface area of a triangular prism, you need to calculate the area of each face and then add them together.
The surface area of a triangular prism consists of:
- Two triangular bases
- Three rectangular faces
1. Area of the triangular bases:
Base of triangle = (1/2) * base * height
Base = x = 8 units
Height = h = 5 units
Area of triangle = (1/2) * 8 * 5 = 20 square units
Area of both triangular bases = 2 * 20 = 40 square units
2. Area of the three rectangular faces:
- The first rectangular face has dimensions of x (8 units) by y (12 units), so its area is 8 * 12 = 96 square units
- The second rectangular face has dimensions of y (12 units) by z (17 units), so its area is 12 * 17 = 204 square units
- The third rectangular face has dimensions of x (8 units) by z (17 units), so its area is 8 * 17 = 136
3. Add up the areas of the triangular bases and the three rectangular faces:
Total surface area = 40 (trianuglar bases) + 96 + 204 + 136 (rectangular faces) = 476 square units
Therefore, the closest option to the calculated surface area of the 3D triangular prism shown above is 468 square units.