SOLUTION: the corner of a triangular base of a truncated prism is defined by A, B, and C. what is its volume if the length of AB =10 ft, BC = 9ft and CA is 12 ft. the sides at A, B and C are

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Question 1178407: the corner of a triangular base of a truncated prism is defined by A, B, and C. what is its volume if the length of AB =10 ft, BC = 9ft and CA is 12 ft. the sides at A, B and C are perpendicular to the triangular base and have the height of 8.6 ft, 7.1 ft and 5.5 ft, respectively.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
the vertices of a triangular base of a truncated prism is defined by A, B, and C.
what is its volume if the length of AB =10 ft, BC = 9ft and CA is 12 ft.
the sides at A, B and C are perpendicular to the triangular base and have the height
of 8.6 ft, 7.1 ft and 5.5 ft, respectively.
~~~~~~~~~~~~~~~


The volume of a truncated triangular prim is

    V = ,

where A the area of a right section (the base) and e1, e2 e3 are the lengths of the lateral edges. 



So, calculate the base area using the Heron's formula and given base edges 10 ft, 9 ft and 12 ft.


You may use this online calculator

https://keisan.casio.com/exec/system/1223267646



It will give you the base area of  44.039 ft^2.



Then multiply this area by   = 7.066 ft.


You will get the volume of your truncated prism of  V = 44.039 * 7.066 = 311.17 ft^3.    ANSWER

Solved.



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