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Answer: The average age is 7.1 years.
This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.
To start, lets multiply the total number of children by their individual ages.
6 x 5 = 30 years
14 x 8 = 112 years
There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.
So the formula for the area of a trapezium is
area = (a + b)/2 * h
*a is the short side
* b is the long side
*h is the height
so let's plug in the values we already know: area, long base, short base. Here's how the formula looks now...
6550 = (150 + 85)/2 * h
*so, we need to find 'h'
use algebra to find it.
6550 = (235/2) * h
6550 = 117.5 * h
6550/117.5 = h
h = 55.74 (approx)
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