Question
What is the surface area of the triangular prism whose net is show?
12 cm.
9 cm
15 cm
4 cm.
12 cm.
9 cm
15 cm
4 cm.
Answers
GPT 3.5
To find the surface area of a triangular prism, we need to calculate the area of each individual face and then add them up.
First, we need to find the area of the two triangular faces. The formula for the area of a triangle is (base x height) / 2.
The base of the triangle is 9 cm and the height is 12 cm.
Area of one triangle = (9 x 12) / 2 = 54 cm^2
Since there are two triangular faces, the total area of the triangles is 2 x 54 = 108 cm^2.
Next, we need to find the area of the three rectangular faces. The formula for the area of a rectangle is length x width.
There are two rectangular faces with dimensions 12 cm x 15 cm and one with dimensions 9 cm x 12 cm.
Area of the two long rectangular faces = 2 x (12 x 15) = 360 cm^2
Area of the short rectangular face = 9 x 12 = 108 cm^2
Total area of the rectangular faces = 360 + 108 = 468 cm^2
Finally, the total surface area of the triangular prism is the sum of the areas of all five faces:
108 (triangles) + 468 (rectangular faces) = 576 cm^2
Therefore, the surface area of the triangular prism is 576 cm^2.
First, we need to find the area of the two triangular faces. The formula for the area of a triangle is (base x height) / 2.
The base of the triangle is 9 cm and the height is 12 cm.
Area of one triangle = (9 x 12) / 2 = 54 cm^2
Since there are two triangular faces, the total area of the triangles is 2 x 54 = 108 cm^2.
Next, we need to find the area of the three rectangular faces. The formula for the area of a rectangle is length x width.
There are two rectangular faces with dimensions 12 cm x 15 cm and one with dimensions 9 cm x 12 cm.
Area of the two long rectangular faces = 2 x (12 x 15) = 360 cm^2
Area of the short rectangular face = 9 x 12 = 108 cm^2
Total area of the rectangular faces = 360 + 108 = 468 cm^2
Finally, the total surface area of the triangular prism is the sum of the areas of all five faces:
108 (triangles) + 468 (rectangular faces) = 576 cm^2
Therefore, the surface area of the triangular prism is 576 cm^2.