Question

What is the area of triangle UVW

Answer 1

This is a polygon with vertices on the lattice.  Let's use Pick's Theorem,

A = (1/2) B + I - 1

where A is the area, B is the number of lattice points on the boundary and I is the number of lattice points in the interior.

In addition to the 3 vertices there are 3 more boundary points on UV and 6 more on WV, none on UV, B=3+3+6=12.   In the interior I count I=9 lattice points.

A = (1/2) 12 + 9 - 1 = 14

Answer: 14

Obviously they just want us to say this is a right triangle, so the legs are altitude and base,

A = (1/2) b h (1/2) |UW| |WV| = (1/2) (4) (7) = 14

That checks.