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

Pythagorean theorem is the base for the right triangle calculator.

  1. Truncated cone 3
    kuzel_komoly_1 The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
  2. Rectangle 35
    rectangles_13 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
  3. Roof 7
    pyramid_in_cube_1 The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
  4. Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  5. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  6. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  7. Hexagonal prism
    hexa_prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
  8. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  9. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  10. 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.
  11. 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.
  12. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  13. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  14. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  15. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 55 dm.
  16. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 18 cm.
  17. 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?
  18. Acreage
    parcela What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
  19. Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm.
  20. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?

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