Answer:
2 m
Explanation:
You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.
Volume
The volume formula for the triangular prism is ...
V = Bh . . . . the product of the triangle area and the base–base distance
12.6 = B·4.5
2.8 = B . . . . . . . area of the triangular base
Area
The area of the triangular base is given by ...
A = 1/2bh
The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...
2.8 = 1/2(2.8)h
2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h
The center height of the tent is 2 meters.
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Additional comment
If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.
V = 1/2LWH
12.6 = 1/2(4.5)(2.8)h = 6.3h
2 = h . . . . meters