[ Home ] [ Squares & Rectangles ] [ Circles ] [ Triangles ] [ Parallelograms ] [ Trapezoids ] [ Cubes ] [ Spheres ] [ Rectangular Solids ] [ Cylinders ] [ Ellipses ] [ Regions In A Plane ] [ Diagonals Of A Polygon ] [ Interior/Exterior Angles ] [ Determining Triangles ] [ Polyhedrons ]

(*View/Download .pdf file*)

Determining How Many Regions In A Plane:

A.  On a number sense test, there will be two scenarios:

1.  No 3 lines are concurrent

2.  Only 3 lines are concurrent

B.  Formulas

1.  In the case for no 3 lines being concurrent, the formula is: n^th triangular number + 1.

2.  In the case for only 3 lines being concurrent, the formula is: n^th triangular number.

Note:  See Triangular Numbers.

C.  Examples

Ex [1]  How many regions in a plane are determined by 5 lines, no 2 are parallel and no 3 are concurrent?  ____.

a.  The answer is the 5^th triangular number plus 1 or 15+1 = 16.

b.  The answer is 16.

Ex [2]  How many regions in a plane are determined by 8 lines, no 2 are parallel and only 3 are concurrent? ____.

a.  The answer is the 8^th triangular number or 36.

b.  The answer is 36.

Back to top