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

  1. Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  2. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle
  3. Cuboidal room
    Cuboid_simple_1 Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
  4. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  5. Axial cut of a rectangle
    cylinder_cut Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
  6. Find diagonal
    diagonal_3 Find diagonal of cuboid with length=20m width=25m height=150m
  7. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  8. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  9. Waste
    doska_kruh How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
  10. 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.
  11. Garden
    garden_1 Area of 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?
  12. Right Δ
    ruler Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  13. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
  14. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  15. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  16. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  17. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  18. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  19. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
  20. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.

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Pythagorean theorem is the base for the right triangle calculator.