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.

Correct answer:

S =  722

Step-by-step explanation:

a1=19 S1=a12=192=361 d1=a1=19 d1=2a2  a2=d1/2=19/213.435 S2=a22=13.4352=3612=18012=180.5  q=S2/S1=180.5/361=12=0.5  S=S1 11q=361 110.5=722   Verifying Solution:  d2=a2=13.43513.435 d2=2a3  a3=d2/2=13.435/2=192=912=9.5 S3=a32=9.52=3614=9014=90.25  q2=S3/S2=90.25/180.5=12=0.5



Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 2 comments:
#
Ann
I don't believe this answer is correct. The ratio (q) to find the area of the next square should be 1/8, not 1/2.

#
Math student
no it is 1/2

avatar







Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Recursion squares
    squares_reccurent 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 peri
  • Infinite sum of areas
    height-of-equilateral-triangle 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
  • Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
  • Sum of GP members
    exponentialFexsDecay Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
  • Rhombus and inscribed circle
    rhombus 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.
  • Squares above sides
    pataVysky Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. 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
  • Covid-19 spread
    covid19 A Street has 13 houses in a row. Some resident sin the first house tested positive for Covid-19. The virus spreads in 2 ways: It can spread to the next house or jump directly to the third house. Residents of house 2 can get infected in only one way, house
  • An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
  • Ratio of sides
    described_circle2 Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  • Find the 13
    circle_inside_rhombus Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
  • Horses playground
    kone_dzokej The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
  • Quarter circle
    quarter_circle What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  • Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  • Equilateral triangle
    3angle_in_circle How long should the minimum radius of the circular plate be cut an equilateral triangle with side 19 cm from it?
  • Inscribed rectangle
    circle_desc_rectangular The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
  • Ratio of sides 2
    square The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
  • Concentric circles
    chord In the circle with diameter, 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.