# Recursion squares

In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 20 cm.

Calculate:

a) the sum of perimeters of all squares

b) the sum of the area of all squares

Calculate:

a) the sum of perimeters of all squares

b) the sum of the area of all squares

## Correct answer:

Tips for related online calculators

See also our right triangle calculator.

Do you want to convert length units?

See also our trigonometric triangle calculator.

Do you want to convert length units?

See also our trigonometric triangle calculator.

### You need to know the following knowledge to solve this word math problem:

**algebra**- geometric progression
- infinite geometric series
**arithmetic**- square root
- addition
**planimetrics**- Pythagorean theorem
- right triangle
- area of a shape
- perimeter
- triangle
- square

### Units of physical quantities:

### Grade of the word problem:

## Related math problems and questions:

- In an

In an ABCD square, n interior points are chosen on each side. Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square. - Difference 66354

A circle is inscribed in a square with a side of 12 cm so that it touches all its sides. Calculate the difference between the area of the square and the circle. - Percentage 80164

I was given a square ABCD 4.2 cm. Find the set of all points that have a distance less than or equal to 2 cm from one of its vertices and lie inside this square. Indicate how much of the square this area occupies as a percentage. - Square and circles

The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.

- N points on the side

An equilateral triangle A, B, and C on each of its inner sides lies N=13 points. Find the number of all triangles whose vertices lie at given points on different sides. - Hypotenuse 82158

A right triangle with hypotenuse c=25 dm is given. Calculate the length of the missing side, given: side a=15 dm. Find the area of this triangle. Sketch the triangle and describe all its vertices and sides correctly. - Infinity

A square with a side 19 long is an inscribed circle, and the circle is inscribed next square, circle, and so on to infinity. Calculate the sum of the area of all these squares.