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 triangles if the ABC triangle has a length? And?

Result

s =  1.732 a2

Solution:

Solution in text s =







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

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

Next similar examples:

  1. Triangular prism
    prism_rt Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
  2. Pyramid height
    pyramid333 Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
  3. Right Δ
    ruler A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  4. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
  5. Perimeter of RT
    triangle_rt1 Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
  6. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  7. Garden
    garden_1 Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
  8. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  9. Square
    square_1 Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
  10. Rhombus
    rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
  11. A photograph
    photo A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
  12. Rectangular garden 2
    garden A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
  13. Iceberg
    ice What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
  14. Concentric circles
    medzikruzie2 There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
  15. Percent change
    rectangles If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
  16. Masquerade ball
    klobouk Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
  17. Scale
    pool_1 Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?