# Recursion squares

In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 42 cm.

Calculate:

a) the sum of perimeters of all squares

b) the sum of area of all squares

Calculate:

a) the sum of perimeters of all squares

b) the sum of area of all squares

**Result****Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):**

**Showing 0 comments:**

**Be the first to comment!**

#### To solve this example are needed these knowledge from mathematics:

## Next similar examples:

- Infinity

In a square with side 8 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares. - Right angled

From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square? - Euklid4

Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle. - Isosceles IV

In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - Six terms

Find the first six terms of the sequence a1 = -3, an = 2 * an-1 - Theorem prove

We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started? - Geometric progression 2

There is geometric sequence with a_{1}=5.7 and quotient q=-2.5. Calculate a_{17}. - Series and sequences

Find a fraction equivalent to the recurring decimal? 0.435643564356 - Triangle ABC

In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC. - Length IT

Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm - Euclid2

In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle. - ABS CN

Calculate the absolute value of complex number -15-29i. - Isosceles III

The base of the isosceles triangle is 17 cm area 416 cm^{2.}Calculate the perimeter of this triangle. - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Equilateral triangle v2

Equilateral triangle has a perimeter 36 dm. What is its area? - The ditch

Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?