The formula for Picks theorem is
A= i + (b/2) -1 where: i=lattice points where grid lines intersect b= number of boundary points To solve for polygon A , Q and R, you would substitute the values into the formula. A(A)= 25 + (12/2) -1 A(A)= 30 A(Q)= 10 + (12/2) -1 A(Q)= 15 A(R)= 11 + (10/2) -1 A(R)= 15 Looking at the areas, you can see that A= Q + R because 30=15 + 15 It is possible to prove that the calculated areas are correct by using other methods. Fro one, you could draw a shape around the polygon, and calculate the area of the shapes around the polygon and subtract that number from the area of the shape. The number you get should equal the area. ex: The area of the rectangle around polygon A = 48 The added areas of the shapes around the polygon=18 And 48-18=30, which was the previously calculated area for polygon A You could also calculate the area by drawing a shape inside the shape and then adding that area to the areas of the other shapes not in the rectangle. ex: drawing a trapezoid in polygon A splits in into 1 rectangle and 2 triangles The area of the trapezoid= 22 The areas of the other shapes=8 And 22+8=30 which is the previously calculated area of polygon A The difference between these methods and Pick's Theorem is that Pick's calculates just the area of the polygon, while the other methods calculate different areas and add or subtract them to make the polygon's shape.
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AuthorIsabel Benak Archives
September 2018
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