The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is tru...

Question

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

A. The circle has the largest area
B. The square has the largest area
C. The equilateral triangle has the largest area
D. All the three shapes have the same area

Accepted Answer

The circle has the largest area — Option A When shapes share the same perimeter (isoperimetric condition), the circle always encloses the greatest area. Among polygons, more sides means more area, so the square beats the triangle. The circle, with infinitely many sides, beats them all.

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true? A. The circle has the largest area B. The square has the largest area C. The equilateral triangle has the largest area D. All the three shapes have the same area