Solve for the surface area of the triangular prism.
(1 point)
Responses
180 square centimeters
180 square centimeters
260 square centimeters
260 square centimeters
320 square centimeters
320 square centimeters
280 square centimeters
To find the surface area of a triangular prism, you need to find the area of each triangular face and rectangular face, and then add them together.
First, calculate the area of the triangular faces:
Area of a triangle = 0.5 * base * height
Triangle 1:
Base = 6 cm
Height = 9 cm
Area = 0.5 * 6 * 9 = 27 square cm
Triangle 2:
Base = 6 cm
Height = 9 cm
Area = 0.5 * 6 * 9 = 27 square cm
Next, calculate the area of the rectangular faces:
Rectangle 1:
Length = 8 cm
Width = 6 cm
Area = length * width = 8 * 6 = 48 square cm
Rectangle 2:
Length = 8 cm
Width = 6 cm
Area = length * width = 8 * 6 = 48 square cm
Now, add the areas of all the faces together:
27 + 27 + 48 + 48 = 150 square cm
Therefore, the surface area of the triangular prism is 150 square centimeters.
dats not one of the answers
Apologies for the previous error in my calculation. Let's reevaluate the surface area of the triangular prism.
The formula for finding the surface area of a triangular prism is:
Surface Area = 2 * (area of the base triangle) + (perimeter of base triangle) * (height of the prism)
Given that the base triangle has a base of 6 cm and height of 9 cm, and the height of the prism is also 9 cm, we can calculate the surface area as follows:
Area of the base triangle = 0.5 * 6 cm * 9 cm = 27 square cm
Perimeter of the base triangle = 6 cm + 6 cm + 9 cm = 21 cm
Surface Area = 2 * 27 square cm + 21 cm * 9 cm
Surface Area = 54 square cm + 189 square cm
Surface Area = 243 square cm
Therefore, the correct answer is that the surface area of the triangular prism is 243 square centimeters.