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Perimeter from coordinates worksheets

A figure on a grid, its corners labeled, and no side lengths printed. These free printable worksheets ask for the perimeter, so each side has to be worked out from the points first. Four figures a page, with an answer key.

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Perimeter from coordinates
Perimeter from coordinates worksheet — First quadrant, whole-number sides, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Some sides can be counted along the grid and some cannot. In a triangle with corners at (1, 1), (9, 1) and (5, 4) the bottom side is plainly 8, but the two slanted sides each need the Pythagorean theorem, and each comes out at 5. The perimeter is 18. Every side on this sheet works out to a whole number, so the arithmetic never gets in the way of the idea.

Why this sheet works

The figures are rectangles, right triangles, isosceles triangles, trapezoids and a tilted figure that sits on its corner. The tilted one is the test, since no side lies along a grid line, and a child who counts squares instead of using the distance will get it wrong. This page stays in the first quadrant; the maker can spread the figures across all four.

How this one works

(1, 1) (9, 1) (5, 4)

(1, 1)to(9, 1)=8
(9, 1)to(5, 4)=5
(5, 4)to(1, 1)=5
8 + 5 + 5=18 units
  1. (1, 1) to (9, 1) is level: 9 − 1 = 8.
  2. (9, 1) to (5, 4) slants: 4 across and 3 up make a right triangle, so 4² + 3² = 5², and the side is 5.
  3. (5, 4) to (1, 1) slants: 4 across and 3 up make a right triangle, so 4² + 3² = 5², and the side is 5.
  4. The perimeter is all 3 sides added: 18 units.

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