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Pick’s Theorem

The shapes below are drawn on a square dotty grid. As well as the dots that are located on their perimeter, some shapes enclose dots within their boundary. By drawing shapes of your own (at least 10) and tabulating results, investigate the relationship between, A (the area enclosed by a shape), P (the number of dots on the perimeter) and I (the number of dots inside the shape). API 1½31 Note that it is often easier to work out the area of some shapes by considering the rectangle that bounds it as indicated for the triangle below. 1 1 ½ 4 – 2½ = 1½

Pick’s Theorem The shapes below are drawn on a square dotty grid. As well as the dots that are located on their perimeter, some shapes enclose dots within their boundary. By drawing shapes of your own (at least 10) and tabulating results, investigate the relationship between, A (the area enclosed by a shape), P (the number of dots on the perimeter) and I (the number of dots inside the shape). API 1½ Have you discovered Pick’s Theorem? A = ½p + I -1

Pick’s Theorem A = ½p + I -1 Use Pick’s Theorem to work out the area of the two shapes below. A = ½ x – 1 = 10½ A = ½ x – 1 = 7½

Dotty