Mensuration
156. The Rectangle's Area · length times breadth, every time
The area is always the product of length and breadth.
Area of a rectangle = length × breadth = l × b. Measured in square units. Drag a corner — the area changes as either dimension changes.
What this lesson covers
Try to break it
Drag C to stretch or shrink the rectangle. The length l, breadth b, and area l × b all update together. Try to find a corner position where the area isn't l × b — impossible.
How you build it
Construct a rectangle.
- Mark point A anywhere on the canvas.
- Mark point B to the right of A — AB will be the length l.
- Draw segment AB — the base of the rectangle.
- Drop a perpendicular at A.
- Drop a perpendicular at B.
- Open compass to breadth b. Place at A and cut an arc on the perpendicular — this marks D.
- Mark point D — where the arc meets the perpendicular at A.
- With the same radius, place compass at B and cut an arc on the perpendicular — this marks C.
- Mark point C — where the arc meets the perpendicular at B.
- Join D and C — the rectangle ABCD is complete.
The proof, step by step
Prove that the area of a rectangle is length × breadth.
- A rectangle has length l and breadth b.
- Imagine filling it with 1×1 unit squares.
- Each row has l squares, and there are b rows.
- Total squares = l × b. So, Area = l × b.
Worked example
A rectangular garden has a length of 12 m and a breadth of 8 m. Find its area.
Area = length × breadth = 12 m × 8 m = 96 m².
- 96 m² — correct
- 40 m²
- 20 m²
- 100 m²