# 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 to related online calculators

Pythagorean theorem is the base for the 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:

## Related math problems and questions:

- Infinity

In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares. - Infinite sum of areas

Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr - Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm^{2}. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area? - Two squares

Two squares whose sides are in the ratio 5:2 have a sum of its perimeters 73 cm. Calculate the sum of the area of these two squares. - Sum of series

Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+.... - 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 the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte - 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. - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2}. Calculate content of square over the triangle's hypotenuse. - Square circles

Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm. - Rectangular trapezoid

The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the - Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Medians in RT

The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is: - Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals. - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle. - Rectangle diagonals

It is given a rectangle with an area of 24 cm^{2}a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Triangle - is RT?

Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.