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.
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)
1 answer