To find the surface area of a triangular prism, we need to calculate the area of each face and then add them together.
The net of a triangular prism consists of 5 faces: 3 rectangular faces and 2 triangular faces.
1. The two triangular faces are congruent right triangles with base = height = 6 ft and a hypotenuse of 10 ft, using the Pythagorean theorem (a2 + b2 = c2), we find the height of the triangle:
62 + b2 = 102
36 + b2 = 100
b2 = 64
b = 8 ft
The area of one triangular face = (1/2) * base * height = (1/2) * 6 * 8 = 24 ft²
Since there are two triangular faces, the total area contributed by the triangular faces is 2 * 24 = 48 ft²
2. The three rectangular faces each have dimensions of 6 ft by 10 ft, so the area of each rectangular face = length * width = 6 * 10 = 60 ft²
Since there are three rectangular faces, the total area contributed by the rectangular faces is 3 * 60 = 180 ft²
Adding the areas of all 5 faces together:
48 ft² (from the triangular faces) + 180 ft² (from the rectangular faces) = 228 ft²
Therefore, the surface area of the triangular prism is 228 ft².
Using the net of the triangular prism, what is its surface area?
(1 point)
○ 240 ft²
1,200 ft."
○ 720 AL."
840 ft."
1 answer
1 answer