What's the surface area of the triangular prisim
The sides are 17m 17m 15m 11m and 16m
To find the surface area of a triangular prism, we need to calculate the area of each of the 5 faces and then sum them up:
1. Area of the triangular base:
The base of the prism is a triangle with sides 17m, 17m, and 15m. We can use Heron's formula to find the area of the triangle:
s = (17 + 17 + 15) / 2 = 24.5m
Area = sqrt(24.5 * (24.5 - 17) * (24.5 - 17) * (24.5 - 15)) = 127.98 m^2
2. Area of the other triangular face:
This face is also a triangle with sides 11m, 16m, and the slant height. Let's calculate the slant height using the Pythagorean theorem:
s^2 = 11^2 + 16^2
s = sqrt(121 + 256) = sqrt(377) ≈ 19.4m
Using Heron's formula:
Area = sqrt(23 * (23 - 16) * (23 - 11) * (23 - 19.4)) = 58.06 m^2
3. Area of the rectangular faces:
There are three rectangular faces with areas:
- 17m * 15m = 255 m^2
- 17m * 11m = 187 m^2
- 15m * 11m = 165 m^2
Summing up the areas of all faces:
127.98 + 58.06 + 255 + 187 + 165 = 793.04 m^2
Therefore, the surface area of the triangular prism is approximately 793.04 square meters.
The options are
768
790
822
779
Adding all the calculations, we have the following:
- Area of the triangular base: 127.98 m^2
- Area of the other triangular face: 58.06 m^2
- Area of the rectangular faces: 255 m^2, 187 m^2, 165 m^2
Adding all these together: 127.98 + 58.06 + 255 + 187 + 165 = 793.04 m^2
Therefore, the closest option to the calculated surface area of the triangular prism is 790.