Free printable resources · Original practice
One cell is one centimeter along each side. Count lengths, compare areas, and work through a notched rectangle with a separate solution.
One cell is one centimeter along each side. Count lengths, compare areas, and work through a notched rectangle with a separate solution.
| Paper | Line interval | Complete cells | Grid width × height |
|---|---|---|---|
| US Letter | 10 mm | 19 × 22 | 190.000 × 220.000 mm |
| A4 | 10 mm | 18 × 24 | 180.000 × 240.000 mm |
Counts describe complete cells between lines. The grid is centered in a region inset 12.7 mm at the sides and 25.4 mm at top and bottom. Physical printing has not been tested on your printer; verify the calibration before measuring.
Draw a 6 cm by 4 cm rectangle. Remove a 2 cm by 1 cm notch from its upper-right corner. Find the remaining area and perimeter.
Worked result
Area = 6 x 4 - 2 x 1 = 22 square centimeters. Perimeter = 6 + 3 + 2 + 1 + 4 + 4 = 20 cm.
The supplied worksheet has space for your drawing and calculations. The separate answer traces the completed shape. Keep the same units through the calculation; square units measure area, while plain units measure length.
Original practice with a separate reference answer. Choose Letter or A4.
Before starting your geometry practice, ensure your printer settings are correct. Select the file matching your paper size, either Letter or A4, and choose actual size printing to avoid scaling errors. Once printed, examine the calibration bars located on the sheet. These bars allow you to confirm that the line-to-line spacing is exactly ten millimeters. If the bars do not match the expected length, adjust your printer settings and reprint. Check both horizontal and vertical dimensions. A matching bar is a useful scale check, although it cannot rule out every printer defect elsewhere on the page.
Locate a clear section of your centimeter graph paper to begin drawing. Count six spaces horizontally and four spaces vertically to establish the dimensions of your main shape. Use a ruler to connect these points, creating a rectangle that measures six centimeters by four centimeters. Ensure your lines align precisely with the grid lines to maintain accuracy. This base shape serves as the foundation for the next step. By counting the spaces between the lines, you confirm the correct dimensions before proceeding to modify the shape with the required notch.
Identify the upper-right corner of your drawn rectangle. From this corner, count two spaces to the left and one space down to define the notch boundaries. Draw lines to remove this two centimeter by one centimeter section. After completing the shape, calculate the area by counting the whole cells inside the figure, which should total twenty-two square centimeters. Then, trace the outer edge to count the perimeter, verifying it equals twenty centimeters. This process reinforces the relationship between grid counting and geometric measurement.
| Watch for | Check instead |
|---|---|
| Printing the file with fit-to-page scaling enabled, which alters the ten millimeter grid spacing and distorts measurements. | Always select actual size or one hundred percent scaling in your print dialog to preserve the correct line-to-line distance. |
| Counting the lines themselves instead of the spaces between them when measuring lengths on the graph paper. | Focus on the empty squares between the grid lines, as each space represents one centimeter of length. |
| Calculating the area of the full rectangle without subtracting the removed notch section from the total count. | Count only the whole cells that remain inside the final shape to get the correct twenty-two square centimeter area. |
Before you begin
Choose the Letter file if you use standard US paper, which provides nineteen columns and twenty-two rows. Select the A4 file for international paper sizes, offering eighteen columns and twenty-four rows.
Measure the supplied 100 mm and 4 inch bars with a physical ruler, and check a perpendicular grid span too. Ten centimeter intervals should span 100 mm. If the axes differ, investigate printer distortion before measuring a drawing.
The final shape, which is a six by four centimeter rectangle with a two by one centimeter notch removed, has an area of twenty-two square centimeters and a perimeter of twenty centimeters.
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Choose a simple rectangular object with whole-centimeter sides, such as a card, a tray base, or a shelf label, and add one internal feature like a corner notch or a divider. Record each side length and state the feature's position as a distance from a named corner, for example two centimeters from the top-left corner along the top edge.
Decide where the outline sits on the sheet and how many complete cells surround it. Because the grid is inset from the paper edges, count only complete cells between printed lines. Mark the plan lightly at grid intersections, then darken the final outline once the counts agree with the written plan.
A drawing is correct when each measured edge equals its planned length and parallel sides remain parallel. Split a notched outline into rectangles along grid lines and add the cell counts to find area; this avoids forcing one rectangle formula onto a shape that is not a rectangle. For perimeter, add the lengths of the actual outline edges, including the two short edges created by a corner notch.
Record both the planned figures and the counted figures side by side so a mismatch is visible. If they differ, the usual cause is a corner placed off an intersection or an edge counted one cell short, not a wrong plan.
Redraw the same object at half the planned lengths where whole centimeters allow. A 12 cm by 8 cm rectangle becomes 6 cm by 4 cm, so area falls from 96 square centimeters to 24 square centimeters while the shape stays similar. This tests whether you can transfer proportions rather than copy counts.
Write the scale on the sheet, for example one grid cell represents one centimeter at half scale. Without that note, a later reader cannot tell whether the drawing shows the object or a reduced version, and measurements become ambiguous.
Plan and draw a rectangle 7 cm by 4 cm with a 2 cm by 1 cm notch removed from one corner, then verify area and perimeter by counting.
Draw the 7 cm by 4 cm rectangle from a grid intersection, then remove a 2 cm by 1 cm rectangle at one corner. The remaining area is 28 minus 2, which is 26 square centimeters. The outline edges are 7, 4, 5, 3, 2, and 1 centimeters; their sum is 22 centimeters, the same as the original rectangle because the notch replaces two outer segments with two inner segments of equal length. Count cells and edge lengths on the sheet to confirm both figures.
Print at 100% and compare a known length against the calibration bar before measuring. If the bar does not match, adjust the print scale and reprint.
Yes, but edges will not follow grid lines exactly. State the fractional lengths and treat cell counting as an approximation.
Usually a corner is off an intersection or an edge was counted one cell short. Re-check each edge against the written plan before changing the plan.
