Paint squares and see two numbers change: the space inside (area) and the distance around (perimeter). Play, solve missions, crack puzzles and beat the clock.
Start here. Cover a shape with little squares. How many squares fit inside? That number is the area. Now walk around the outside edge and count every side of every square you pass. That number is the perimeter. Area is about the space inside. Perimeter is about the distance around.
Rectangles. A rectangle 4 squares long and 3 squares wide has 3 rows of 4 squares, so its area is 4 × 3 = 12. To walk around it you go 4 + 3 + 4 + 3 = 14 steps, so its perimeter is 14. Two rectangles can have the same perimeter but very different areas. Two shapes can also have the same area but different perimeters.
Stretching a shape. A long thin rectangle has a long perimeter for its area. A square-like rectangle holds the most area for a given fence. That is why a farmer with 20 m of fence gets the biggest field from a 5 m by 5 m square.
L-shapes. Split an L into two rectangles and add their areas. Or draw the big rectangle around it and take away the missing corner. For the perimeter of an L, walk all six sides: it equals the perimeter of the big rectangle around it. If one side is missing, use the other sides: the top plus the notch must add up to the bottom.
Try this above. In Play, paint a 2 by 6 rectangle, then paint a 3 by 4 rectangle. Which has the bigger area? Which has the bigger perimeter? Then paint a shape with a hole in the middle and see what happens to the perimeter.
Area is how many squares cover the inside of a shape. Perimeter is the total length of the edges around it. Area is measured in square units such as cm². Perimeter is measured in plain units such as cm.
In this game the perimeter counts every edge between a filled square and an empty square, so the edges around a hole count too. Think of a fence around the shape and a fence around the hole.
For a fixed perimeter, the more equal the length and width, the larger the area. With 20 m of fence: 1 × 9 gives 9 m², 3 × 7 gives 21 m², 5 × 5 gives 25 m².
Just starting: count squares on small shapes. I know the basics: rectangles, area = length × width, perimeter = 2 × (length + width). Challenge me: L-shapes, missing sides and shapes that need both area and perimeter.
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