Pythagorean theorem - examples - page 23

  1. ABCD square
    s1 In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
  2. Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  3. The perimeter
    hexagon6 The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
  4. Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  5. Equilateral triangle
    equilateral_triangle2_1 Calculate the area of an equilateral triangle with circumference 72cm.
  6. Bamboo
    Bambus Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
  7. Sphere from tree points
    sphere2_1 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  8. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  9. Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  10. Quadrangular pyramid
    jehlan_4b_obdelnik_1 Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
  11. Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  12. Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
  13. Is right-angled
    rt_sqrt_2 Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle?
  14. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  15. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  16. Body diagonal
    diagonal_1 Calculate the length of the body diagonal of the 6cm cube.
  17. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  18. Cone 15
    cone_9 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
  19. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  20. Construct
    kosodlznik3 Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.

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Pythagorean theorem is the base for the right triangle calculator.