Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.

Correct answer:

a =  4.0825 cm
S =  196.6326 cm2
V =  166.6667 cm3

Step-by-step explanation:

v=10 cm θ=60 °  tanθ=v:u  u=v/tanθ°=v/tan60° =10/tan60° =10/1.732051=5.7735 cm  u=2a  a=u/2=5.7735/2=4.0825 cm
S1=a2=4.08252=50316.6667 cm2 S2=4 a v=4 4.0825 10163.2993 cm2  S=2 S1+S2=2 16.6667+163.2993=196.6326 cm2
V=S1 v=16.6667 10=166.6667 cm3



Did you find an error or inaccuracy? Feel free to write us. Thank you!






avatar




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions:

  • Quadrilateral prism
    hranol4sreg Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
  • Angle of diagonal
    hranol The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
  • 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.
  • Prism diagonal
    hranol222 The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
  • Tetrahedral pyramid
    pyramid_4s Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm2, and the deviation angle of the side edges from the plane of the base is 60 degrees.
  • Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
  • Quadrilateral pyramid
    jehlan3 In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
  • Regular quadrangular pyramid
    6 How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
  • Quadrangular prism
    hranol4sreg Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
  • Tetrahedral pyramid
    jehlan It is given a regular tetrahedral pyramid with a base edge of 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
  • Pyramid 8
    ihlan Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
  • Side edges
    jehlan The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
  • Quadrilateral pyramid
    jehlan_4b_obdelnik The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
  • Glass
    pohgar How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
  • Base diagonal
    jehlan_4b_obdelnik In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
  • Regular square prism
    cuboid_3colors The volume of a regular square prism is 192 cm3. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
  • 4side pyramid
    ihlany Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.