The perimeter is just how many units it is all the way around
the quadrilateral.  You can get 3 of the sides just by counting
the blocks on the graph paper.

From S to V is 9 units straight down.
From V to U is 12 units left to right.
From U to T is 4 units straight up.

The only line that we have to calculate is the slanted one from S to T.

We do that by drawing a horizontal line from T over to the line SV, like
below.  We will label the point W(-5,-2) where it intersects line SV:



To calculate to upper side ST of the quadrilateral, we use the
Pythagorean theorem on right triangle SWT, which states that



We count blocks and get that WT = 12, the same as VU. And we
see that SW is 5 unit long, by counting blocks.

So we substitute 12 for SW and 5 for WT









From the calculator we can get that square
root to be 13.

Then the perimeter is the sum of all four
sides:

SV + VU + UT + ST = 9 + 12 + 4 + 13 = 38

So the perimeter is 38.

Edwin