Pythagorean theorem + expression of a variable from formula - problems - page 4

  1. Cube diagonals
    krychlicka_1 Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
  2. Rectangle 3-4-5
    diagonal_rectangle_1 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
  3. Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  4. Two cyclists
    compass_1 Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
  5. Billiard balls
    balls_billiard A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
  6. Quadrangular prism
    hranol4sreg_7 Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
  7. Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  8. Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
  9. 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.
  10. Four sided prism
    hranol4sreg Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
  11. Billboard
    rectangle_3 Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard.
  12. Diagonal of the rectangle
    rectangle_1 Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
  13. 30-gon
    30gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
  14. Two diagonals
    rhombus-diagonals The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
  15. Cuboid easy
    cuboid_11 The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
  16. Land - isosceles trapezoid
    lichobeznik-stredni_pricka_1 Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
  17. Diagonals of diamond
    kosostvorec_4 Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
  18. Church roof 2
    skleneny-kuzel The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
  19. Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  20. The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?

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Pythagorean theorem is the base for the right triangle calculator.