Worksheets · Pre-Algebra

Perimeter and area in the coordinate plane worksheet for Pre-Algebra

In Pre-Algebra these shapes sit on the grid: rectangles, right triangles and trapezoids with sides along the grid lines. Subtract coordinates to get those sides, use the Pythagorean theorem for a slanted side, then apply the usual perimeter and area rules.

Also taught in Geometry, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Perimeter and Area in the Coordinate Plane

Date Period

Find each measure.

  1. Find the perimeter from the vertices

    Find the perimeter of the rectangle with vertices (2,−3), (5,−3), (5,2), (2,2).
  2. Find the perimeter of the rectangle with vertices (−2,0), (6,0), (6,3), (−2,3).
  3. Find the perimeter of the rectangle with vertices (3,0), (7,0), (7,8), (3,8).
  4. Find the perimeter of the rectangle with vertices (−3,−4), (−1,−4), (−1,1), (−3,1).
  5. Find the perimeter of the rectangle with vertices (2,−4), (9,−4), (9,−2), (2,−2).

  1. Find the area from the vertices

    Find the area of the triangle with vertices (3,0),(15,0),(3,16).
  2. Find the area of the triangle with vertices (−4,−11), (4,−11), (−4,4).
  3. Find the area of the triangle with vertices (11,−5), (20,−5), (11,7).
  4. Find the area of the triangle with vertices (−5,10), (4,10), (−5,22).
  5. Find the area of the triangle with vertices (−12,−6), (−4,−6), (−12,9).

  1. Find the perimeter with the distance formula

    Find the perimeter of the triangle with vertices (−3,1), (−6,1), (−3,5).
  2. Find the perimeter of the triangle with vertices (2,−2), (14,−2), (2,−7).
  3. Find the perimeter of the triangle with vertices (−4,0), (−12,0), (−4,−6).
  4. Find the perimeter of the triangle with vertices (−5,−2), (−2,−2), (−5,2).
  5. Find the perimeter of the triangle with vertices (3,2),(15,2),(3,−3).

  1. Find a quadrilateral's area from its vertices

    Find the area of the trapezoid with vertices (−3,1), (5,1), (1,5), (−1,5).
  2. Find the area of the trapezoid with vertices (2,1), (10,1), (7,8), (2,8).
  3. Find the area of the trapezoid with vertices (−4,−6), (5,−6), (4,1), (−1,1).
  4. Find the area of the trapezoid with vertices (1,−2), (10,−2), (7,4), (3,4).
  5. Find the area of the trapezoid with vertices (−1,−2), (7,−2), (9,1), (2,1).

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Perimeter and Area in the Coordinate PlaneAnswer keyVersion 2

Date Period

Find each measure.

  1. Find the perimeter from the vertices

    Find the perimeter of the rectangle with vertices (2,−3), (5,−3), (5,2), (2,2).16
  2. Find the perimeter of the rectangle with vertices (−2,0), (6,0), (6,3), (−2,3).22
  3. Find the perimeter of the rectangle with vertices (3,0), (7,0), (7,8), (3,8).24
  4. Find the perimeter of the rectangle with vertices (−3,−4), (−1,−4), (−1,1), (−3,1).14
  5. Find the perimeter of the rectangle with vertices (2,−4), (9,−4), (9,−2), (2,−2).18

  1. Find the area from the vertices

    Find the area of the triangle with vertices (3,0),(15,0),(3,16).96
  2. Find the area of the triangle with vertices (−4,−11), (4,−11), (−4,4).60
  3. Find the area of the triangle with vertices (11,−5), (20,−5), (11,7).54
  4. Find the area of the triangle with vertices (−5,10), (4,10), (−5,22).54
  5. Find the area of the triangle with vertices (−12,−6), (−4,−6), (−12,9).60

  1. Find the perimeter with the distance formula

    Find the perimeter of the triangle with vertices (−3,1), (−6,1), (−3,5).12
  2. Find the perimeter of the triangle with vertices (2,−2), (14,−2), (2,−7).30
  3. Find the perimeter of the triangle with vertices (−4,0), (−12,0), (−4,−6).24
  4. Find the perimeter of the triangle with vertices (−5,−2), (−2,−2), (−5,2).12
  5. Find the perimeter of the triangle with vertices (3,2),(15,2),(3,−3).30

  1. Find a quadrilateral's area from its vertices

    Find the area of the trapezoid with vertices (−3,1), (5,1), (1,5), (−1,5).20
  2. Find the area of the trapezoid with vertices (2,1), (10,1), (7,8), (2,8).45.5
  3. Find the area of the trapezoid with vertices (−4,−6), (5,−6), (4,1), (−1,1).49
  4. Find the area of the trapezoid with vertices (1,−2), (10,−2), (7,4), (3,4).39
  5. Find the area of the trapezoid with vertices (−1,−2), (7,−2), (9,1), (2,1).22.5

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the perimeter of the rectangle with vertices (1,2), (7,2), (7,6), (1,6)

  1. Width: 7 - 1 = 6. Height: 6 - 2 = 4.
  2. Perimeter: 2(6 + 4) = 20.

The answer is 20.

Where students go wrong

Counting grid points instead of spaces. From x = 1 to x = 7 is 6 units, not 7.

Also called area from coordinates, perimeter from vertices or coordinate geometry area.

What you can put on this worksheet

Perimeter from the vertices
Find the perimeter of the rectangle with vertices (−1,0), (6,0), (6,2), (−1,2). → 18
Area from the vertices
Find the area of the triangle with vertices (1,3),(7,3),(1,11). → 24
Slanted sides, with the distance formula
Find the perimeter of the triangle with vertices (−1,−1), (4,−1), (−1,11). → 30
Quadrilaterals from the vertices
Find the area of the parallelogram with vertices (−2,−1), (6,−1), (7,3), (−1,3). → 32

Questions about these worksheets

Yes. Every perimeter and area in the coordinate plane sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the perimeter and area in the coordinate plane questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: perimeter from the vertices, area from the vertices, slanted sides, with the distance formula and quadrilaterals from the vertices. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the coordinates instead of subtracting them. A side length is the difference between two coordinates, never the sum, and it is always positive.