How to Find the Area of the Region Bounded by Rectangular Grid

Step-by-Step Guide

1. 1

   Step 1: Write down the formula A=B2+I−1{\displaystyle A={\frac {B}{2}}+I-1}.

     This formula is used to find the area of the region bounded by grids where B{\displaystyle B} is the number of boundary points and I{\displaystyle I} equals the number of interior points.
   
   In this case, you have an irregular hexagon.
2. 2

   Step 2: To find B{\displaystyle B}

     In other words, count the number of the points that one of the sides of the polygon passes through.  The number of boundary points do not have to equal the number of sides of the polygon.
   
   In the example, count seven boundary points.  They are colored blue. , I{\displaystyle I} can even be 0{\displaystyle 0}.
   
   In the example, you see that there are seven.  The interior points are colored red. ,  The answer to the equation is your final answer.
   
   Since B=7{\displaystyle B=7} and I=7{\displaystyle I=7}, A=B2+I−1{\displaystyle A={\frac {B}{2}}+I-1} becomes 72+7−1=3.5+7−1=10.5−1=9.5.9.5{\displaystyle {\frac {7}{2}}+7-1=3.5+7-1=10.5-1=9.5.9.5} is our answer!
3. 3

   Step 3: count the number of boundary points.

4. 4

   Step 4: Count the number of points that are inside of the polygon to find I{\displaystyle I}.

5. 5

   Step 5: Plug the numbers in the formula and solve the equation.

Detailed Guide

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