Answer:
The height of the trapezoidal base is 7.2 ft.
Step-by-step explanation:
Consider the provided information.
The volume of trapezoidal prism is the area of the cross-section × the length.
[tex]V=BH[/tex]
Where B is the area of base, H is the length and V is the volume.
The length of the prism is 25.2ft and volume is 1279.152
[tex]1279.152=B(25.2)[/tex]
[tex]B=50.76[/tex]
Hence, the base area is 50.76 ft².
The base is trapezoid.
The area of trapezoid is [tex]B=\frac{1}{2}(b_1+b_2)h[/tex]
Substitute B=50.76, [tex]b_1=10\ and\ b_2=4.1[/tex] in above formula.
[tex]50.76=\frac{1}{2}(10+4.1)h[/tex]
[tex]50.76=7.05h[/tex]
[tex]h=7.2[/tex]
Hence, the height of the trapezoidal base is 7.2 ft.
