What Hierarchy?

Probability Level 1

How many trapezoids are there in the figure above?

Bonus : Generalize this.

9 10 11 12

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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3 solutions

Sudoku Subbu
Jun 25, 2016

In the given Triangle there are 10 Trapezoids. 4 − T r a p e z o i d s − − − − − − − > 1 − c o m p o n e n t 4-Trapezoids------->1 -component 3 − T r a p e z o i d s − − − − − − > 2 − C o m p o n e n t s 3-Trapezoids------> 2 -Components 2 − T r a p e z o i d s − − − − − − > 3 − C o m p o n e n t s 2-Trapezoids------>3- Components 1 − T r a p e z o i d − − − − − − − − − − − − − − > 4 − C o m p o n e n t s 1- Trapezoid--------------> 4 -Components

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Colin Carmody
Jun 12, 2016

To count the trapeziods, you have to keep adding 1+2+3+4+...+n where n is the number of sections in the larger figure, not including the top triangle. This is equivalent to adding numbers 1 to n, so we can use the formula (1+n)/2*n.

In the figure shown, n=4, so the solution is 10. If you were to count the trapeziods by hand, you would get this result as well.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Denis Herda
Jun 12, 2016

Choose two of paralel segments for one trapezoid. If there are n segments, count combinations of 2 segments from n segments.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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