Area from coordinatesFirst quadrant
Name: Date:
Find the area of the shaded figure from the points.
1 square units
2 square units
3 square units
4 square units
Area from coordinates worksheets
The corners are labeled and the figure is shaded, but no lengths are printed. These free printable worksheets ask for the area, so a child has to pull the base and the height out of the coordinates. Four figures a page, with an answer key.
If they get stuck
Area from coordinates
The answer key prints on a separate page.
What's on this sheet
Rectangles and right triangles come first because their sides lie along the grid. A triangle with corners at (4, 4), (6, 4) and (6, 1) has a base of 2 and a height of 3, so its area is 3 square units. The flatter triangles ask a better question. With corners at (1, 1), (1, 9) and (5, 7) the base is the upright side of length 8, and the height is how far the third corner sits from it, which is 4.
Why this sheet works
The tilted square is the one that needs real thought. Its corners at (6, 2), (9, 6), (5, 9) and (2, 5) sit off the grid lines, so the side has to come from the distance between two corners. The side is 5 and the area is 25, even though the figure looks as if it might be measured some other way. This page stays in the first quadrant; the maker can use all four.
How this one works
(4, 4) (6, 4) (6, 1)
2and3
2 × 3 ÷ 2=3 square units
- One side along the grid is 2 and the other is 3: read both by subtracting the points.
- A triangle's area is half of base times height: 3 square units.