Answer:
B. [tex]755\text{ cm}^2[/tex]; [tex]785\text{ cm}^2[/tex].
Step-by-step explanation:
We have been given a triangular prism and we are asked to find the lateral surface are of the prism.
We know that lateral surface area of prism equals to the product of perimeter of base of prism and height of prism.
[tex]LSA=p\times h[/tex], where,
p = Perimeter of base,
h = Height of the prism.
We will find the perimeter of triangular base of the given prism as:
[tex]5\text{ cm}+6\text{ cm}+11.21\text{ cm}=22.21\text{ cm}[/tex]
[tex]LSA=22.21\text{ cm}\times 34\text{ cm}[/tex]
[tex]LSA=755.14\text{ cm}^2\approx 755\text{ cm}^2[/tex]
Therefore, the lateral surface area of our given prism is [tex]755\text{ cm}^2[/tex].
The surface area of the given prism will be equal to the sum of area of each face of the prism.
[tex]\text{Area of triangular faces}=2\times (\frac{1}{2}\times 5\text{ cm}\times 6\text{ cm})[/tex]
[tex]\text{Area of triangular faces}=30\text{ cm}^2[/tex]
[tex]\text{Area of base rectangular faces}=34\text{ cm}(6\text{ cm}+5\text{ cm}+11.21\text{ cm})[/tex]
[tex]\text{Area of base rectangular faces}=34\text{ cm}(22.21\text{ cm})[/tex]
[tex]\text{Area of base rectangular faces}=755.14\text{ cm}^2[/tex]
[tex]\text{Total surface area}=755.14\text{ cm}^2+30\text{ cm}^2[/tex]
[tex]\text{Total surface area}=785.14\text{ cm}^2\approx 785\text{ cm}^2[/tex]
Therefore, option B is the correct choice.
