To find the area of the triangular base of the prism, we need to find the area of the triangle formed by the 6 cm, 4 cm, and 12 cm sides. We can use the formula for the area of a triangle:
Area = 1/2 * base * height
The base and height of the triangle are 4 cm and 6 cm, respectively.
Area = 1/2 * 4 cm * 6 cm = 12 square cm
Therefore, the area of the triangular base of the prism is 12 square centimeters.
To find the area of the smallest rectangle of the prism, we can use the formula for the area of a rectangle:
Area = length * width
The dimensions of the smallest rectangle are 4 cm and 7 cm.
Area = 4 cm * 7 cm = 28 square cm
Therefore, the area of the smallest rectangle of the prism is 28 square centimeters.
To find the area of the largest rectangle of the prism, we can use the same formula:
Area = length * width
The dimensions of the largest rectangle are 7 cm and 12 cm.
Area = 7 cm * 12 cm = 84 square cm
Therefore, the area of the largest rectangle of the prism is 84 square centimeters.
The total surface area of the triangular prism can be calculated by adding the areas of the two triangles and three rectangles:
Total Surface Area = 2 * (Area of triangular base) + (Area of smallest rectangle) + (Area of largest rectangle) + (Area of lateral faces)
Total Surface Area = 2 * 12 square cm + 28 square cm + 84 square cm
Total Surface Area = 24 square cm + 28 square cm + 84 square cm
Total Surface Area = 136 square cm
Therefore, the total surface area of the triangular prism is 136 square centimeters.
A triangular prism is shown
Angles: 7 cm 7 cm 6 cm 4 cm 12 cm
Determine the area of the triangular base of the prism blank square centimeters
Determine the area of the smallest rectangle of the prism, blank square centimeters
Determine the area of the large rectangle of the prism, blank square centimeters
What is the total surface area of the triangular, prism, blank square centimeters
3 answers
Are you sure?
I apologize for the mistake in my previous response. Let's correct the calculations:
- The area of the triangular base of the prism is 12 square centimeters (as calculated previously).
- The area of the smallest rectangle of the prism is 4 cm * 7 cm = 28 square centimeters.
- The area of the largest rectangle of the prism is 7 cm * 12 cm = 84 square centimeters.
Now, let's calculate the total surface area of the triangular prism:
The lateral faces of the prism consist of two triangles and three rectangles. The two triangles each have an area of 1/2 * base * height, which is 1/2 * 6 cm * 4 cm = 12 square centimeters each.
Each rectangular face can be calculated as length * width:
- Two rectangles are 7 cm * 12 cm = 84 square centimeters each.
- One rectangle is 4 cm * 12 cm = 48 square centimeters.
Therefore, the total surface area of the triangular prism should be calculated as follows:
Total Surface Area = 2(12 square cm) + 2(84 square cm) + 48 square cm
Total Surface Area = 24 square cm + 168 square cm + 48 square cm
Total Surface Area = 240 square cm
Therefore, the correct total surface area of the triangular prism is 240 square centimeters. Thank you for prompting for the verification.
- The area of the triangular base of the prism is 12 square centimeters (as calculated previously).
- The area of the smallest rectangle of the prism is 4 cm * 7 cm = 28 square centimeters.
- The area of the largest rectangle of the prism is 7 cm * 12 cm = 84 square centimeters.
Now, let's calculate the total surface area of the triangular prism:
The lateral faces of the prism consist of two triangles and three rectangles. The two triangles each have an area of 1/2 * base * height, which is 1/2 * 6 cm * 4 cm = 12 square centimeters each.
Each rectangular face can be calculated as length * width:
- Two rectangles are 7 cm * 12 cm = 84 square centimeters each.
- One rectangle is 4 cm * 12 cm = 48 square centimeters.
Therefore, the total surface area of the triangular prism should be calculated as follows:
Total Surface Area = 2(12 square cm) + 2(84 square cm) + 48 square cm
Total Surface Area = 24 square cm + 168 square cm + 48 square cm
Total Surface Area = 240 square cm
Therefore, the correct total surface area of the triangular prism is 240 square centimeters. Thank you for prompting for the verification.