Answer:
240 in²
Step-by-step explanation:
The prism has an isosceles triangle with the following data:
- Two lengths = 5 inches
- Other length = 8 inches
- Height = 12 inches
Since the prism consist of 2 triangle bases and three rectangular faces, the surface area (SA) of the prism can be calculated as follows:
![SA = SA_{b1} + SA_{b2} + SA_{f1} + SA_{f2} + SA_{f3}](https://tex.z-dn.net/?f=%20SA%20%3D%20SA_%7Bb1%7D%20%2B%20SA_%7Bb2%7D%20%2B%20SA_%7Bf1%7D%20%2B%20SA_%7Bf2%7D%20%2B%20SA_%7Bf3%7D%20)
Where:
and
are the surface areas of the two triangle bases.
,
and
: are the surface areas of the three rectangular faces.
The surface area of the triangle bases can be calculated as follows:
![SA_{b1} = SA_{b2} = \frac{b*h}{2}](https://tex.z-dn.net/?f=%20SA_%7Bb1%7D%20%3D%20SA_%7Bb2%7D%20%3D%20%5Cfrac%7Bb%2Ah%7D%7B2%7D%20)
Where:
b: is the base = lenght of 8 inches
h: is the height = 3 inches
![SA_{b1} = SA_{b2} = \frac{8*3}{2} = 12 in^{2}](https://tex.z-dn.net/?f=%20SA_%7Bb1%7D%20%3D%20SA_%7Bb2%7D%20%3D%20%5Cfrac%7B8%2A3%7D%7B2%7D%20%3D%2012%20in%5E%7B2%7D%20)
Now, we need to find the surface area of the rectangular faces using the following data:
Rectangular face 1 = rectangular face 2:
- One side = 12 inches
- Other side = 5 inches
Rectangular face 3:
- One side = 12 inches
- Other side = 8 inches
Hence, the SA of the rectangular face 1 and rectangular face 2 is:
![SA_{f1} = SA_{f2} = 12*5 = 60 in^{2}](https://tex.z-dn.net/?f=%20SA_%7Bf1%7D%20%3D%20SA_%7Bf2%7D%20%3D%2012%2A5%20%3D%2060%20in%5E%7B2%7D%20)
And the SA of the rectangular face 3 is:
![SA_{f3} = 12*8 = 96 in^{2}](https://tex.z-dn.net/?f=%20SA_%7Bf3%7D%20%3D%2012%2A8%20%3D%2096%20in%5E%7B2%7D%20)
Finally, the SA of the prism is:
![SA = SA_{b1} + SA_{b2} + SA_{f1} + SA_{f2} + SA_{f3}](https://tex.z-dn.net/?f=%20SA%20%3D%20SA_%7Bb1%7D%20%2B%20SA_%7Bb2%7D%20%2B%20SA_%7Bf1%7D%20%2B%20SA_%7Bf2%7D%20%2B%20SA_%7Bf3%7D%20)
Therefore, the surface area of the prism is 240 in².
I hope it helps you!