In the figure shown here, the distance between any two horizontally or vertically adjacent dots is one unit. What is the area of the shaded polygon in square units?

sudsw12 Apr 19, 2019

#1**+1 **

The easiest thing here is to use something known as "Pick's Theorem"....this only works when the vertexes of the figure are lattice points

Lattice point = a point with integer coordinates

Area =

Number of lattice points on the boundary of the figure / 2 + number of interior lattice points - 1

So we have

Boundary lattice points = 9

Interior lattice points = 17

Area = 9/2 + 17 - 1 = 4.5 + 16 = 20.5 units^2

CPhill Apr 19, 2019