# 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 = 22 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**- 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. - 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. - Perimeters 81399

Two squares are given. The first has a side length of 5 cm, the second 10 cm. Write the ratio of: for a- of their sides for b- their perimeters for c- their areas - Triangle 3552

Draw a circle k (S, r = 3cm). Build a triangle ABC so that its vertices lie on the circle k and the length of the sides is (AB) = 2.5 cm (AC) = 4 cm - Two squares

Two squares with sides in the ratio 5:2 have a sum of their perimeters 73 cm. Calculate the sum of the area of these two squares. - Squares ratio

The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of these squares. (Write the ratio in the basic form). (Perimeter = 4 * a, area S = a²) - Infinite sum of areas

An equilateral triangle A1B1C1 is constructed above the height of the equilateral triangle ABC is constructed as. Above the height of the equilateral triangle A1B1C1 is built triangle A2B2C2, and so on. The procedure is repeated continuously. What is the - Interior angles

In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees, and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Isosceles 5666

In the isosceles trapezoid ABCD, calculate the missing side length "a" and its areas. Side b = d = 50 cm, c = 20 cm, height = 48 cm. - Calculate 2416

In the rectangle ABCD we know the side length AB = 16 cm and the diagonal AC = 20 cm. Calculate its perimeter and area. - Triangle in a square

In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Right-angled 66344

From a square with a side of 4 cm, we cut four right-angled isosceles triangles with right angles at the square's vertices and with an overlap of √2 cm. We get an octagon. Calculate its perimeter if the area of the octagon is 14 cm². - Determine 36601

The plumbers have to cut sheet metal measuring 220 cm and 308 cm into squares of equal size so that the squares are as large as possible and the sheet metal is used without residue. How many such squares will they cut? Determine the side of this square.