Area calculations

Area is a measure of the size of a two-dimensional region. For standard shapes, we use specific formulas. For more complex shapes, we can decompose them into simpler shapes or use coordinate geometry.

Important properties

• Area is always non-negative.

• Area is additive: the area of a union of non-overlapping regions is the sum of their areas.

• Formulas: Rectangle ($A = ab$), Triangle ($A = \frac{1}{2}bh$), Parallelogram ($A = bh$), Trapezium ($A = \frac{1}{2}(a+b)h$), Circle ($A = \pi r^2$).

• Area can be estimated or calculated exactly depending on the shape.