9th grade (14y) + Pythagorean theorem - examples

Pythagorean theorem is the base for the right triangle calculator.

  1. Right triangle eq2
    rt_2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
  2. Rhombus and diagonals
    kosostvorec_2 The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
  3. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  4. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  5. Right Δ
    ruler Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  6. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  7. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  8. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  9. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 91 dm.
  10. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  11. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  12. Circle chord
    circleChord What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm?
  13. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
  14. Acreage
    parcela What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
  15. Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 6 cm and 3 cm.
  16. Garden
    garden_1 Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
  17. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 15 cm and 27 cm long.
  18. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  19. Spherical cap
    kulova_usec From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere?
  20. Prism
    prism-square The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?

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