Corrected Question
The triangular prism shown has 1, 2, 3 or 5 triangular faces and 1,2,3, or 5 lateral faces.
The area of one triangular face is 7.5,8.125,15,or 17 ![mm^2](https://tex.z-dn.net/?f=mm%5E2)
The surface area of the triangular prism is 55.5,127.5,135,or 150 ![mm^2](https://tex.z-dn.net/?f=mm%5E2)
Answer:
(B)2 triangular faces
(C)3 lateral faces.
(A)Area of one Triangular Face ![=7.5mm^2](https://tex.z-dn.net/?f=%3D7.5mm%5E2)
(C)Total Surface Area of the Triangular prism ![=135mm^2](https://tex.z-dn.net/?f=%3D135mm%5E2)
Step-by-step explanation:
The triangular prism is attached.
The triangular prism shown has 2 triangular faces and 3 lateral faces.
Base of the triangle =2.5mm
Height of the Triangle =6mm
Area of one Triangular Face ![=\frac{1}{2}*6*2.5=7.5mm^2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%2A6%2A2.5%3D7.5mm%5E2)
The dimensions of the lateral rectangles are:
- 2.5 mm by 8mm
- 6 mm by 8mm
- 6.5 mm by 8mm
Therefore, total surface area of the triangular prism
=2(Area of one Triangular Face)+Area of 3 rectangular faces
![=2(7.5)+ (2.5 X 8+ 6 X 8 + 6.5 X 8)\\=15+120\\=135mm^2](https://tex.z-dn.net/?f=%3D2%287.5%29%2B%20%282.5%20X%208%2B%206%20X%208%20%2B%206.5%20X%208%29%5C%5C%3D15%2B120%5C%5C%3D135mm%5E2)
Total Surface Area of the Triangular prism ![=135mm^2](https://tex.z-dn.net/?f=%3D135mm%5E2)