Answer:
V = 1,728 mi³
SA = 864 mi²
Explanation:
We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.
First, we can solve for the area of one of the triangle sides:
A(triangle) = (1/2) · b · h
A(triangle) = (1/2) · 24 · 18
A(triangle) = 12 · 18
A(triangle) = 216 mi²
Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.
V = A(triangle) · depth
V = 216 · 8
V = 1,728 mi³
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We can find the surface area by finding the area of each side, then adding all of those areas together.
We already know that the area of each of the triangle sides is 216 mi².
Now, we can solve for the area of the base.
A(base) = length · width
A(base) = 24 · 8
A(base) = 192 cm²
Then, we can find the area of the top side.
A(top) = length · width
A(top) = 30 · 8
A(top) = 240 mi²
Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.
SA = (2 · A(triangle)) + A(base) + A(top)
SA = 2(216) + 192 + 240
SA = 432 + 192 + 240
SA = 624 + 240
SA = 864 mi²