Answer:
416 in²
Explanation:
You want the surface area of an isosceles triangular prism of length 10 in that has a triangular base with a base of 12 in and a height of 8 in.
Area
The area of the prism is the sum of the areas a of the two triangular bases and the three rectangular faces.
The triangle area is given by ...
A = 1/2bh
Then the area of the two identical triangles is ...
A = bh = (12 in)(8 in) = 96 in²
The area of the three rectangular faces is ...
A = ∑LW = (12 in)(10 in) +(10 in)(10 in) +(10 in)(10 in) = (12 +10 +10)(10) in²
A = 320 in²
So, the total area is ...
surface area = base area + face area
surface area = 96 in² +320 in² = 416 in²
The surface area is 416 square inches.
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