Free printable resources · Original practice
Count square units inside each outline and unit lengths around its boundary. Keep area in square units and perimeter in units.
Free area and perimeter drawing worksheets with original orthogonal regions, notches and stepped outlines. Letter/A4 student sheets and answers included.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Given information | Task |
|---|---|---|
| AP01 | Vertices in order: A(0, 0); B(5, 0); C(5, 3); D(0, 3). | Draw the boundary, then calculate its area and perimeter. Show a decomposition or count grid squares. |
| AP02 | Vertices in order: A(0, 0); B(5, 0); C(5, 2); D(2, 2); E(2, 5); F(0, 5). | Draw the boundary, then calculate its area and perimeter. Show a decomposition or count grid squares. |
| AP03 | Vertices in order: A(0, 0); B(6, 0); C(6, 3); D(4, 3); E(4, 5); F(0, 5). | Draw the boundary, then calculate its area and perimeter. Show a decomposition or count grid squares. |
| AP04 | Vertices in order: A(0, 0); B(3, 0); C(3, 4); D(1, 4); E(1, 2); F(0, 2). | Draw the boundary, then calculate its area and perimeter. Show a decomposition or count grid squares. |
Use the coordinates, dimensions and rules given for each case. Distances and areas are measured in grid units.
AP01: Rectangle five by three
| Step | Worked result |
|---|---|
| 1 | Area = 15 square units. |
| 2 | Boundary lengths: 5 + 3 + 5 + 3 = 16 units. |
The first case shows the checking pattern. Individual answer files contain the completed graph or net and result for every case.
Plot each vertex in order on a coordinate grid, then connect consecutive points with straight segments, including the last point back to the first. For AP01, plot A(0,0), B(5,0), C(5,3), D(0,3) and connect A-B-C-D-A. Check that each segment is horizontal or vertical by comparing coordinates: same y means horizontal, same x means vertical. Label each side length directly on the drawing. This boundary is the path you will measure for perimeter and the outline that encloses the area.
Split the shape into non-overlapping rectangles using the given vertices. For AP02, separate the 5-by-2 rectangle (area 10) and the 2-by-3 rectangle (area 6), giving 16 square units. For AP03, use a 6-by-3 rectangle (18) plus a 4-by-2 rectangle (8), totaling 26. For AP04, use a 3-by-2 rectangle (6) plus a 2-by-2 rectangle (4), totaling 10. Alternatively, count grid squares inside the boundary. Record each rectangle's dimensions and partial area before adding.
Perimeter is the sum of all outer side lengths, not the sum of rectangle areas. Measure each segment from the coordinates: horizontal length is the difference in x, vertical length is the difference in y. For AP01, add 5+3+5+3=16 units. For AP02, add 5+2+3+3+2+5=20 units. For AP03, add 6+3+2+2+4+5=22 units. For AP04, add 3+4+2+2+1+2=14 units. Write each length on the matching side before summing so no segment is counted twice or missed.
| Watch for | Check instead |
|---|---|
| Counting interior decomposition lines as part of the perimeter. | Perimeter uses only the outer boundary segments. Interior lines used to split the shape into rectangles are not added to the perimeter sum. |
| Assuming equal slopes always mean the lines are parallel without checking intercepts. | Equal slopes with different intercepts give parallel lines. Equal slopes with equal intercepts describe the same line, not two parallel lines. |
| Using a slope product of 1 as the test for parallel lines. | A slope product of -1 tests perpendicularity. Parallel lines require equal slopes and distinct intercepts; a product of 1 is not the parallel criterion. |
Choose the PDF that matches your paper. Print at Actual size / 100% and turn off Fit, Shrink and browser headers. SVG is editable but an editor can rescale it; the PDF is the simpler print route.
Connect them in the order listed, then close the shape by joining the last vertex to the first. For AP01, that means A to B to C to D and back to A. Check that each segment is horizontal or vertical by comparing coordinates.
Yes. Count the full unit squares inside the boundary. For AP02 the count is 16, for AP03 it is 26, and for AP04 it is 10. Decomposing into rectangles gives the same totals and shows the arithmetic clearly.
Area measures square units inside the shape, while perimeter measures linear units along the outer boundary. For AP01 the area is 15 square units but the perimeter is 16 units, found by adding the side lengths 5+3+5+3.
Yes. The individual student, reference and answer files plus collection packs are free without signup. Credit Zumola under CC BY 4.0 when sharing or adapting.
The diagrams and exercises on this page are original Zumola resources.
