"Published in Newark, California, USA"
A dam 100 ft. long has a cross section which is a trapezoid whose altitude is 16 ft., and whose upper base is 5 ft. If the lower base angles of the cross section are 50° and 65°, find the volume of material the dam contains.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
Since the length of the lower base is not given, then we have to isolate the base first and then label further so that we can solve for its length.
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| Photo by Math Principles in Everyday Life |
Consider the 50° right triangle,
Consider the 65° right triangle,
The length of the lower base of a trapezoid which is the cross section of a dam is
Hence, the area of the base is
Therefore, the volume of a trapezoid prism which is a dam is
