Inequalities with areas

Geometric inequalities with areas involve proving that the area of one figure is greater than, less than, or equal to the area of another figure, often under certain conditions. These inequalities can be used to compare triangles, quadrilaterals, circles, and other plane figures.

Important properties

• If two figures have the same shape and size, their areas are equal.

• Among all rectangles with a fixed perimeter, the square has the largest area.

• Among all triangles with a fixed base and height, the area is the same.

• For a fixed perimeter, the circle has the largest area among all plane figures.