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 total sum of the areas of all triangles if the ABC triangle has a length? And?
Correct answer:
Tips for related online calculators
See also our right triangle calculator.
Calculation of an equilateral triangle.
See also our trigonometric triangle calculator.
Calculation of an equilateral triangle.
See also our trigonometric triangle calculator.
You need to know the following knowledge to solve this word math problem:
algebraarithmeticplanimetricsGrade of the word problem
Related math problems and questions:
- Constructed 77874
Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their areas are the same. - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the - 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 = 20 cm. Calculate: a) the sum of peri - Constructed triangle
The perimeter of the right triangle is 18 cm. The sum of the areas of the squares constructed above its three sides is 128 cm². What is the area of the triangle? - Squares above sides
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. Calcu - construction triangle problem
Construct the vertices C of all triangles ABC, if given side AB, height vb on side b, and length of line tc on side c. Build all the solutions. Mark the vertices C1, C2,. .. - Ratio of triangles areas
In an equilateral triangle ABC, the point T is its center of gravity, the point R is the image of the point T in axial symmetry along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas
