Cut a piece off and slide it across
A leaning mat covers a floor. The mat is a parallelogram, a four-sided shape with opposite sides parallel. Straighten it. Does it cover more, or less?
- A parallelogram, base 8, leaning right.
- Cut straight down, at the top corner.
- Slide the left piece one base length right.
- The pieces fill a rectangle: 8 × 4 = 32.
Cutting and sliding keeps the area
The straightened mat covers the same area, neither more nor less. Nothing is added. Nothing is removed. The two pieces cover what the parallelogram covered. A rectangle appears: 8 × 4 = 32.
Dissection — cut a shape, then rearrange the pieces. The area stays equal.
Rule: area of a parallelogram = base × height.
The base is the side you choose to measure from. The height is the gap from the base to the opposite side. Measure it square across, at a right angle to them. Here the slanted side is 5, but the height is 4. The rule uses 4: the rectangle is 8 wide and 4 tall.
Slide the piece. Watch the shape become a rectangle.
Loading lab…