Area of a shape on a grid – three methods
Work out the area of a shape on a grid. Then you will see three methods: counting squares, rectangle minus the corners cut off, and cutting into strips.
Three methods
How do you play?
You will see a shape on a grid – a rectangle with one or more corners cut off. Each square has an area of 1. Work out the area (pole) of the shape, enter the result and click “Check”. Then you will see three ways to work out the same area. In Poland decimals are written with a comma: 0,25 means 0.25. The game uses the Polish way, as in school and in the exam.
What are the three methods?
Counting squares. Count the whole squares, then the halves. Two halves make one square.
Rectangle minus corners. Work out the area of the rectangle around the shape and subtract what was cut off. A corner with shorter sides 2 and 2 is a triangle with an area of 2 · 2 : 2 = 2 (: means divide).
Cutting into parts. Cut the shape into pieces whose area you know: rectangles, triangles, trapeziums. The area of a trapezium is (a + b) : 2 · h, where a and b are the parallel sides and h is the height.
What is the most common mistake?
Counting every square that is cut as a whole one. A square cut diagonally in half is only a half. Another common mistake is mixing up area and perimeter: the area is the number of squares inside, and the perimeter (obwód) is the length of the edge.
How does this help in the eighth-grade exam?
In 2025 the hardest question in the whole Polish eighth-grade exam paper was question 20 – the area of a polygon found by cutting it into smaller polygons or completing it to a bigger one. The success rate was 29%, and one pupil in four gave a full solution. The game practises exactly these methods.
Curriculum: point XI.5 for grades 4–6 (Polish core curriculum, Dz.U. 2024 poz. 996). Source: CKE report 2025 (in Polish).
Questions about the game
How do you work out the area of a shape on a grid?
There are three methods: count the whole squares and the halves, draw a rectangle around the shape and subtract the corners cut off, or cut the shape into rectangles, triangles and trapeziums.
Why work out the area a second way?
The second method is a check. If both give the same result, you can be sure it is right.
Is the game free?
Yes. You play in the browser, with no sign-up and no e-mail.
Mini glossary: English – Polish
- area – pole
- perimeter – obwód
- square on a grid – kratka
- rectangle – prostokąt
- triangle – trójkąt
- trapezium – trapez
The game runs in your browser. There is no time limit and we save nothing.