1
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Axiom 1: The area of any shape is greater than or equal to zero.

2
00:00:06,900 --> 00:00:12,080
Axiom 2: Two shapes that completely overlap have equal area.

3
00:00:13,683 --> 00:00:18,500
Axiom 3: Shapes placed together without overlapping,

4
00:00:18,600 --> 00:00:21,431
total area equals sum of parts.

5
00:00:23,033 --> 00:00:27,709
Axiom 4: A square with side length 1 has area 1.

6
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These four are the foundation. All area formulas derive from them.

7
00:00:43,583 --> 00:00:49,435
Side equals 1. Area equals 1.

8
00:00:55,933 --> 00:00:59,625
A rectangle with length 3 and width 2.

9
00:01:06,616 --> 00:01:14,388
Area equals 1 plus 1 plus 1 plus 1 plus 1 plus 1, equals 3 times 2.

10
00:01:16,983 --> 00:01:20,483
A rectangle with length 6 and width 4.

11
00:01:39,483 --> 00:01:42,983
A rectangle with length 6 and width 4.

12
00:01:55,083 --> 00:01:58,583
A rectangle with length 8 and width 3.

13
00:02:17,083 --> 00:02:20,583
A rectangle with length 8 and width 3.

14
00:02:31,366 --> 00:02:35,082
A rectangle with length 10 and width 7.

15
00:02:53,566 --> 00:02:57,282
A rectangle with length 10 and width 7.