To find the surface area of the solid figure with an equilateral triangle base, we need to calculate the area of the equilateral triangle base and the lateral surface area of the triangular prism.
The formula to find the area of an equilateral triangle with side length s is:
Area = (sqrt(3) / 4) * s^2
Given the side length of the equilateral triangle is 3.5, the area of the equilateral triangle base is:
Area = (sqrt(3) / 4) * (3.5)^2
Area = (sqrt(3) / 4) * 12.25
Area ≈ 6.70 cm^2
Since the triangular prism has three identical lateral faces, the lateral surface area of the triangular prism is three times the area of the equilateral triangle base:
Lateral Surface Area = 3 * 6.70
Lateral Surface Area = 20.10 cm^2
Therefore, the surface area of the solid figure with an equilateral triangle base is 20.10 cm^2. Since this is not one of the provided answers, the closest option is 19.26 cm^2.
Use the image to answer the question. Find the surface area of the solid figure with an equilateral triangle base. (1 point)
the numbers: 3.5, 3.9, 4.5
wrong answers: 36.41cm ^2, 38.59cm^2, 22.94cm^2, 19.26cm^2, 35.35cm^2, 39.95cm^2.
5 answers
still wrong
I apologize for the error. Let's try a different approach.
The lateral surface area of a triangular prism can be calculated using the formula:
Lateral Surface Area = perimeter of the base * height
Since the base of the prism is an equilateral triangle with side length 3.5, the perimeter of the base is:
Perimeter = 3 * side length
Perimeter = 3 * 3.5
Perimeter = 10.5 cm
Given that the height of the prism is 4.5 cm, the lateral surface area is:
Lateral Surface Area = Perimeter * height
Lateral Surface Area = 10.5 * 4.5
Lateral Surface Area = 47.25 cm^2
Therefore, the correct lateral surface area for the solid figure is 47.25 cm^2. The closest option provided is 39.95 cm^2.
The lateral surface area of a triangular prism can be calculated using the formula:
Lateral Surface Area = perimeter of the base * height
Since the base of the prism is an equilateral triangle with side length 3.5, the perimeter of the base is:
Perimeter = 3 * side length
Perimeter = 3 * 3.5
Perimeter = 10.5 cm
Given that the height of the prism is 4.5 cm, the lateral surface area is:
Lateral Surface Area = Perimeter * height
Lateral Surface Area = 10.5 * 4.5
Lateral Surface Area = 47.25 cm^2
Therefore, the correct lateral surface area for the solid figure is 47.25 cm^2. The closest option provided is 39.95 cm^2.
w r o n g
I apologize for the mistake. Let's try another approach to find the surface area of the solid figure.
The equilateral triangle base has a side length of 3.5 units. To find the area of the equilateral triangle base, we can use the formula:
Area of equilateral triangle = (√3/4) * (side length)^2
Plugging in the side length of 3.5 units:
Area of equilateral triangle = (√3/4) * (3.5)^2
Area of equilateral triangle = (√3/4) * 12.25
Area of equilateral triangle ≈ 6.69 square units
Now, to find the lateral surface area of the triangular prism, we calculate the perimeter of the equilateral triangle base and multiply it by the height of the prism.
Perimeter of equilateral triangle = 3 * side length
Perimeter of equilateral triangle = 3 * 3.5
Perimeter of equilateral triangle = 10.5 units
Lateral surface area = Perimeter of equilateral triangle * Height
Lateral surface area = 10.5 * 4.5
Lateral surface area = 47.25 square units
Therefore, the total surface area of the solid figure with an equilateral triangle base is the sum of the area of the base and the lateral surface area:
Total surface area = Area of equilateral triangle base + Lateral surface area
Total surface area = 6.69 + 47.25
Total surface area ≈ 53.94 square units
Therefore, the surface area of the solid figure is approximately 53.94 square units. Since this is not one of the given options, the closest provided answer is 51.20 square units.
The equilateral triangle base has a side length of 3.5 units. To find the area of the equilateral triangle base, we can use the formula:
Area of equilateral triangle = (√3/4) * (side length)^2
Plugging in the side length of 3.5 units:
Area of equilateral triangle = (√3/4) * (3.5)^2
Area of equilateral triangle = (√3/4) * 12.25
Area of equilateral triangle ≈ 6.69 square units
Now, to find the lateral surface area of the triangular prism, we calculate the perimeter of the equilateral triangle base and multiply it by the height of the prism.
Perimeter of equilateral triangle = 3 * side length
Perimeter of equilateral triangle = 3 * 3.5
Perimeter of equilateral triangle = 10.5 units
Lateral surface area = Perimeter of equilateral triangle * Height
Lateral surface area = 10.5 * 4.5
Lateral surface area = 47.25 square units
Therefore, the total surface area of the solid figure with an equilateral triangle base is the sum of the area of the base and the lateral surface area:
Total surface area = Area of equilateral triangle base + Lateral surface area
Total surface area = 6.69 + 47.25
Total surface area ≈ 53.94 square units
Therefore, the surface area of the solid figure is approximately 53.94 square units. Since this is not one of the given options, the closest provided answer is 51.20 square units.
11 answers