Question

Find the area of the following shape. you must show all work to receive credit.

Answer 1

Answer:

A = 57

Step-by-step explanation:

Use the Pick's theorem

Let P be a polygon in the plane whose vertices have integer coordinates. Then the area of P can be determined just by counting the lattice points on the interior and boundary of the polygon!

In fact, the area is given by

$A=i+\dfrac{b}{2}-1$

where i is the number interior lattice points, and b is the number of boundary lattice points.

Look at the picture.

$i=50,\ b=16$

Substitute:

$A=50+\dfrac{16}{2}-1=50+8-1=57$