Answer:
196 m²
Explanation:
You want the surface area of the isosceles triangular prism with base edges of 8 m and 3 m, and a prism height of 9.1 m.
Base area
The area of a triangular base can be found from side lengths a, b, c using Heron's formula:
A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2
Here, we have ...
s = (3 + 8 + 8)/2 = 9.5
A = √(9.5×6.5×1.5×1.5) = √138.9375 ≈ 11.79 . . . . square meters
Then the area of the two bases is ...
total base area = 2×11.78 m² = 23.57 m²
Lateral area
The lateral area of the prism is the sum of the areas of its rectangular faces. That sum is the product of the prism height and the perimeter of the base.
LA = (9.1 m)(19 m) = 172.9 m²
Surface area
Then the total surface area of the prism is ...
surface area = base area + lateral area
surface area = 23.57 m² +172.9 m² = 196.47 m²
The surface area of the prism is about 196 square meters.
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