Why do squares have the biggest area for their perimeter?

Answer 1

Circles have the biggest area for the same perimeter/circumference.

Perhaps you expected to get the same area with a longer rectangle. To see why this is not so - and help you visualize the problem - considere the following extreme case: a square of 1 x 1, and a "rectangle" of 2 x 0. (Or amost zero width - a very thin approximation will also do.) The perimeter is the same as for the square, but the area is zero (or near zero).

You can do this kind of maximization or minimization problem with calculus. You may learn about this later.

Circles have the biggest area for the same perimeter/circumference.

Perhaps you expected to get the same area with a longer rectangle. To see why this is not so - and help you visualize the problem - considere the following extreme case: a square of 1 x 1, and a "rectangle" of 2 x 0. (Or amost zero width - a very thin approximation will also do.) The perimeter is the same as for the square, but the area is zero (or near zero).

You can do this kind of maximization or minimization problem with calculus. You may learn about this later.

Circles have the biggest area for the same perimeter/circumference.

Perhaps you expected to get the same area with a longer rectangle. To see why this is not so - and help you visualize the problem - considere the following extreme case: a square of 1 x 1, and a "rectangle" of 2 x 0. (Or amost zero width - a very thin approximation will also do.) The perimeter is the same as for the square, but the area is zero (or near zero).

You can do this kind of maximization or minimization problem with calculus. You may learn about this later.

Circles have the biggest area for the same perimeter/circumference.

Perhaps you expected to get the same area with a longer rectangle. To see why this is not so - and help you visualize the problem - considere the following extreme case: a square of 1 x 1, and a "rectangle" of 2 x 0. (Or amost zero width - a very thin approximation will also do.) The perimeter is the same as for the square, but the area is zero (or near zero).

You can do this kind of maximization or minimization problem with calculus. You may learn about this later.

Answer 2

Circles have the biggest area for the same perimeter/circumference.

Perhaps you expected to get the same area with a longer rectangle. To see why this is not so - and help you visualize the problem - considere the following extreme case: a square of 1 x 1, and a "rectangle" of 2 x 0. (Or amost zero width - a very thin approximation will also do.) The perimeter is the same as for the square, but the area is zero (or near zero).

You can do this kind of maximization or minimization problem with calculus. You may learn about this later.