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# Can a circle and a square have the same area?

## Can a circle and a square have the same area?

A square with side length 2 and a circle share the same center. That’s fine. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square.

## Why a square doesn’t equal a circle?

The area of a square is the length of a side times itself. The area of a square with a side of eight is equal to eight squared or 64. Squaring the circle means finding a circle whose area is exactly equal to the area of a square using only a finite number of steps. Therefore, you cannot square a circle.

Why does a circle have more area than a square?

The area of a circle is πr2 , where r is the radius of the circle. The area of a square is s2 , where s is the side length. But s = P/4, so the area of a square is P2 /16. Since 1/(4π) > (1/16), the circle has more area than the square.

### Are square and circle equal?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. The area of a circle of radius r units is A=πr2 . Substitute r=4 in the formula.

### Which shape gives the largest area?

the circle
The shape which has the largest area with a fixed perimeter is the circle, in comparison to the triangle, square and other polygons.

Which is the largest shape?

Rhombicosidodecahedron
References U27, C30, W14
Properties Semiregular convex
Colored faces 3.4.5.4 (Vertex figure)
Deltoidal hexecontahedron (dual polyhedron) Net

## What is nature’s strongest shape?

There are several shapes that are used when strength is important. The arc (think: circle) is the strongest structural shape, and in nature, the sphere is the strongest 3-d shape. The reason being is that stress is distributed equally along the arc instead of concentrating at any one point.

## What shape does not exist in nature?

Mathematical shapes can exist in various dimensions. They can also be defined very specifically. A mathematical circle doesn’t exist in nature because a) it is a two dimensional object and b) shapes in nature are quantised – at some point a flower is made of cells and then atoms.

How is the area of a square equal to that of a circle?

Top Answerer. The relationship is that the perimeter of the square is equal to the circumference of the circle multiplied by 1.13. Thus, p = 1.13 c. Here’s how that’s derived: the circle’s area (πr²) is defined as being equal to the square’s area (4s), where r is the circle’s radius, and s is the square’s side.

### How is the perimeter of a square related to its circumference?

The relationship is that the perimeter of the square is equal to the circumference of the circle multiplied by 1.13. Thus, p = 1.13 c. Here’s how that’s derived: the circle’s area (πr²) is defined as being equal to the square’s area (4s), where r is the circle’s radius, and s is the square’s side.

### Is the quadrature of the circle the same as squaring the circle?

The term quadrature of the circle is sometimes used to mean the same thing as squaring the circle, but it may also refer to approximate or numerical methods for finding the area of a circle .

Is it possible to Squar a circle with a rational number?

It is possible to construct a square with an area arbitrarily close to that of a given circle. If a rational number is used as an approximation of π, then squaring the circle becomes possible, depending on the values chosen.