Foundation
Mathematics Foundation
Area Related to Circle
Surface Area and Volume
Mensuration
Question
A wire of length 2p is bent to form a circle, a triangle, a rectangle and a polygon. State which figure has greatest area
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Solution
For a fixed perimeter, the circle always has the maximum possible area. This is a fundamental principle in mathematics known as the isoperimetric inequality. The area of a circle with circumference (perimeter) P is given by:
Other shapes like triangles, rectangles, and polygons with the same perimeter will always have a smaller area because their geometry is less efficient at enclosing space. Therefore, the circle has the greatest area.
Final answer: circle