Inequalities with areas

Inequalities with areas are statements that compare the areas of different geometric figures, often using algebraic expressions. These inequalities can help us understand limits and relationships between shapes, such as how the area of an inscribed shape compares to the area of the shape it is inside.

Important properties

• If one figure is completely inside another, its area is less than or equal to the area of the larger figure.

• The area of a triangle is always less than or equal to the area of any polygon that contains it.

• For a fixed perimeter, the area of a shape can vary; for example, among all rectangles with a given perimeter, the square has the largest area.