Area measures how much surface a flat shape covers. A rectangle's area is length times width; a triangle's is half the base times the height. The unit is always squared—square meters, square feet, square miles—because you are counting unit squares that fit inside.

Ancient Egyptians and Babylonians computed areas for taxation and construction. Greek geometers formalized the rules. Archimedes went further, using exhaustion to approximate the area of a circle. That method foreshadowed integral calculus.

In practice, area matters for painting walls, buying land, laying carpet, and designing circuit boards. Irregular shapes are handled by dividing them into simpler pieces or by integration. The same idea extends to surface area in three dimensions and to more abstract measures in analysis. Area is one of the first geometric quantities children learn and one of the most widely applied.

• Measures surface coverage of a 2D shape
• Units are squared
• Rectangle: length × width
• Extended by calculus to irregular regions