Calculations at a cash shape. A cash is an ancient Chinese coin that has been used for small amounts of money for thousands of years. It is shaped like a circle with a square hole in the middle.
Enter radius or diameter of the circle and side length of the square, and choose the number of decimal places. Then click Calculate. The side length of the square cannot be larger than the radius of the circle times the root of 2.
Formulas:
d = 2 r
l ≤ √2 * r
p = 2 π r + 4 l
Ac = π r²
Aq = l²
A = Ac - Aq
Kreiszahl pi:
π = 3.141592653589793...
A Chinese bronze 5 cash coin from the Northern Song Dynasty at the time of emperor Huizong, about 1102-1106.
Radius, diameter, length and circumference have the same unit (e.g. meter), the area has this unit squared (e.g. square meter). Perimeter refers to inner and outer boundary lines.
By cutting out a smaller shape from a larger one inside of this, any number of new objects can be created. These can be referred to as two-dimensional shapes with a hole. Their calculation always follows the same principle. The area is, of course, that of the original shape minus that of the cut-out shape. The perimeter, on the other hand, is the sum of both perimeters. While the perimeter is often perceived as the outer boundary line, this length is already the perimeter of the original shape, so the cut-out shape would be ignored. Therefore, if this hole should play a role in the perimeter, it must be added; otherwise, only the larger shape is used for the calculation. By the way, the area of the larger shape is always larger than that of the smaller one, but this does not necessarily apply to the perimeter.
The hole, of course, doesn't have to be exactly in the center, as is the case here. If the cut-out shape lies completely within the outer shape, even if they touch, then the calculation for the area and perimeter is the same. It only becomes more complicated when the two intersect.
Other two-dimensional shapes with a hole are annulus and elliptical ring, whereas for these two, the outer and inner shapes are similar.
