A pillar if length 5 m has a cross section which is uniform & in the shape of a trapezium. [ Rest of the math is in "anything else" section] if the parallel sides of the tropizium are 1 m and 1.5 m long and the distance between the parallel sides is 1 m, find the volume of the pillar.

Expert Answers

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I think the easiest way to solve this problem is to divide the trapezium into two pieces.

The first is a square with all sides being equal to 1 m.

The rest of the trapezium is then a right triangle with a base of .5 m and a height of 1 m. (Note, the 1.5 m long side is broken into 1 m (one side of the square) and .5 m (the base of the triangle).

Now we can do the calculations.

For the square:

First, the area of the square. It is 1 m on each side, so the area is 1 x 1 = 1 sq. m.

Now we can find the volume of that part of the pillar. This is the area of the square (1 sq. m.) times the length (5 m.)

5 m x 1 sq. m = 5 cubic meters

For the triangle:

First, the area of the triangle. The formula is B x H / 2. So, the area is .5 m x 1 m / 2 = .5 m /2 = .25 sq. m.

Now we can find the volume of this part of the pillar.

5 m. x .25 sq. m. = 1.25 cubic meters

Now add the two parts together:

5 cu. m + 1.25 cu. m. = 6.25 cu. m.

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