Free printable resources · Original practice
Plot three ordered pairs, close the outline, classify the triangle from its side or angle evidence and calculate area from a base and height.
Free triangle drawing worksheets on coordinate grids with right, scalene and isosceles examples. Plot, classify and calculate area with separate answers.
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 |
|---|---|---|
| TI01 | Vertices in order: A(0, 0); B(4, 0); C(0, 3). | Plot and join the vertices. Classify by sides and angles; calculate the area. |
| TI02 | Vertices in order: A(0, 0); B(3, 0); C(1, 4). | Plot and join the vertices. Classify by sides and angles; calculate the area. |
| TI03 | Vertices in order: A(0, 0); B(4, 0); C(2, 3). | Plot and join the vertices. Classify by sides and angles; calculate the area. |
| TI04 | Vertices in order: A(0, 0); B(3, 0); C(3, 3). | Plot and join the vertices. Classify by sides and angles; calculate the area. |
Use the coordinates, dimensions and rules given for each case. Distances and areas are measured in grid units.
TI01: Right triangle
| Step | Worked result |
|---|---|
| 1 | Squared side lengths: 16, 25, 9. |
| 2 | Triangle: right and scalene; area = 6 square units. |
The first case shows the checking pattern. Individual answer files contain the completed graph or net and result for every case.
Start by plotting each vertex on the grid using its coordinates. For example, with A(0, 0), B(4, 0), and C(0, 3), mark these points precisely. Then join the points in order to form the triangle. This step ensures you see the shape before calculating. Next, find the squared side lengths using the distance formula or by counting grid squares when sides are horizontal or vertical. For the example, the squared lengths are 16, 25, and 9. These values help classify the triangle and compute the area.
Compare the squared side lengths to classify the triangle. If all three squared lengths are different, the triangle is scalene. If two are equal, it is isosceles. For angles, check the relationship between the squares: if the sum of the two smaller squares equals the largest, it is right; if greater, acute; if less, obtuse. For instance, squared lengths 16, 25, 9 give 16+9=25, so it is right. Lengths 9, 20, 17 give 9+17=26>20, so acute. Lengths 16, 13, 13 give 13+13=26>16, so acute. Lengths 9, 9, 18 give 9+9=18, so right.
For triangles with a horizontal or vertical base, use the base-height formula: area = 1/2 × base × height. Identify the base length by counting squares along the horizontal or vertical side, and the height as the perpendicular distance from the opposite vertex to the base line. For A(0,0), B(4,0), C(0,3), base AB=4, height from C to AB is 3, so area=1/2×4×3=6. For A(0,0), B(3,0), C(1,4), base AB=3, height=4, area=6. For A(0,0), B(4,0), C(2,3), base=4, height=3, area=6. For A(0,0), B(3,0), C(3,3), base=3, height=3, area=9/2.
| Watch for | Check instead |
|---|---|
| Assuming that if two sides are equal, the triangle must be isosceles and acute. | An isosceles triangle can be right, acute, or obtuse. Check the angle using the squared lengths: for 9, 9, 18, 9+9=18, so it is right isosceles, not acute. |
| Using slope product alone to decide if lines are parallel. | Slope product only tests perpendicularity (product = -1). For parallelism, slopes must be equal and intercepts must differ. Equal slopes with equal intercepts describe the same line. |
| Calculating area by counting only whole squares inside the triangle. | Use the base-height formula or decompose into right triangles. Counting squares can miss partial squares and give incorrect results. For example, the triangle with vertices (0,0), (3,0), (1,4) has area 6, not a whole number of squares. |
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Use the squared side lengths. If the sum of the two smaller squared lengths equals the largest squared length, the triangle is right. For example, 16+9=25, so the triangle with squared lengths 16, 25, 9 is right.
Yes. For example, the triangles with vertices (0,0), (4,0), (0,3) and (0,0), (3,0), (1,4) both have area 6 square units, but they are different shapes and classifications.
They are parallel. If the slopes are equal and the intercepts are different, the lines never intersect. If the intercepts are also equal, they are the same line.
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.
