Note: Figure not drawn to scale.
Height has been rounded for computational ease.
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 need to calculate the area of each of the five faces and add them together.
1. The area of the two triangular bases:
Area = 1/2 * base * height
Base of each triangle = X = 8 units
Height of each triangle = h = 5 units
Area = 1/2 * 8 * 5 = 20 square units (for each triangle)
Total for both triangles = 2 * 20 = 40 square units
2. The area of the three rectangular faces:
Rectangular face 1:
Area = length * height
Length = X = 8 units
Height = Y = 12 units
Area = 8 * 12 = 96 square units
Rectangular face 2:
Area = length * height
Length = Z = 17 units
Height = Y = 12 units
Area = 17 * 12 = 204 square units
Rectangular face 3:
Area = length * height
Length = Z = 17 units
Height = h = 5 units
Area = 17 * 5 = 85 square units
Total area of rectangular faces = 96 + 204 + 85 = 385 square units
Adding the areas of the triangular bases and rectangular faces:
Total surface area = 40 + 385 = 425 square units
Therefore, the surface area of the triangular prism is 425 square units.
no
I apologize for the error in my calculation. Let's re-calculate the surface area of the triangular prism with the given dimensions:
1. Area of the two triangular bases:
Base of each triangle = X = 8 units
Height of each triangle = h = 5 units
Area = 1/2 * base * height
Area = 1/2 * 8 * 5 = 20 square units
Total area for both triangles = 2 * 20 = 40 square units
2. Area of the three rectangular faces:
Rectangular face 1:
Area = length * height
Length = X = 8 units
Height = Y = 12 units
Area = 8 * 12 = 96 square units
Rectangular face 2:
Area = length * height
Length = Z = 17 units
Height = Y = 12 units
Area = 17 * 12 = 204 square units
Rectangular face 3:
Area = length * height
Length = Z = 17 units
Height = h = 5 units
Area = 17 * 5 = 85 square units
Total area for the rectangular faces = 96 + 204 + 85 = 385 square units
Adding the areas of the triangular bases and rectangular faces:
Total surface area = 40 + 385 = 425 square units
Therefore, the surface area of the triangular prism with the given dimensions is 425 square units. Thank you for your understanding.
one of these
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 determine the areas of each face and add them up.
1. Area of the two triangular bases:
Base of each triangle = X = 8 units
Height of each triangle = h = 5 units
Area = 1/2 * base * height
Area = 1/2 * 8 * 5 = 20 square units
Total area for both triangles = 2 * 20 = 40 square units
2. Area of the three rectangular faces:
- Rectangle 1:
Length = Z = 17 units
Height = Y = 12 units
Area = Length * Height = 17 * 12 = 204 square units
- Rectangle 2:
Length = X = 8 units
Height = Y = 12 units
Area = Length * Height = 8 * 12 = 96 square units
- Rectangle 3:
Length = Z = 17 units
Height = h = 5 units
Area = Length * Height = 17 * 5 = 85 square units
Total area for the three rectangular faces = 204 + 96 + 85 = 385 square units
The sum of the two triangular bases and the three rectangular faces is:
40 + 385 = 425 square units
Therefore, the surface area of the triangular prism is 425 square units.
Since none of the given options match the calculated value, would you like me to recalculate or verify anything else?
chose one
Apologies for the oversight earlier. From the options provided, the closest value to the calculated surface area of 425 square units is 468 square units. Therefore, the closest option to the calculated surface area of the triangular prism is:
468 square units
Thank you for your patience.