An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.
What is the surface area of the triangular prism?
(1 point)
To find the surface area of the triangular prism, we need to calculate the areas of all the individual faces and add them together.
The formula for the surface area of a triangular prism is:
Surface area = 2(base area of the triangle) + (perimeter of the triangle)(height of the prism) + (area of the rectangular face)
First, let's find the base area of the triangle. We can use the formula for the area of a triangle, which is:
Area = 0.5(base)(height)
Area = 0.5(5)(4)
Area = 10 square centimeters
Now let's find the perimeter of the triangle:
Perimeter = base1 + base2 + hypotenuse
Perimeter = 3 + 4 + 5
Perimeter = 12 centimeters
Now let's find the area of the rectangular face:
Area = width x length
Area = 5 x 11
Area = 55 square centimeters
Now, we can calculate the surface area of the triangular prism:
Surface area = 2(10) + (12)(11) + 55
Surface area = 20 + 132 + 55
Surface area = 207 square centimeters
Therefore, the surface area of the triangular prism is 207 square centimeters.