The tetrahedron

Calculate the surface area and volume of a regular tetrahedron 4.9 cm high, the base edge has a length of 6 cm.

Correct answer:

S =  62.35 cm2
V =  25.46 cm3

Step-by-step explanation:

h=4.9 cm a=6 cm  h12=a2(a/2)2  h1=32 a=32 6=3 3 cm5.1962 cm  S1=a h12=6 5.19622=9 3 cm215.5885 cm2  S=4 S1=4 15.5885=36 3=62.35 cm2
a2=h2+(2/3 h1)2  h=a2(2/3 h1)2=62(2/3 5.1962)2=2 6 cm4.899 cm  V=13 S1 h=13 15.5885 4.899=18 2=25.46 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.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


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

Related math problems and questions:

  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 6 cm.
  • The regular
    hranol3b The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
  • Tetrahedral pyramid
    jehlan A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
  • Pyramid 4sides
    pyramid Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
  • 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.
  • Quadrangular pyramid
    pyramid_4s 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.
  • Triangular pyramid
    tetrahedron1 Calculate the volume and surface area of a regular triangular pyramid with height equal to the base edge 10 cm length.
  • Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
  • Right pyramid
    squarepyramid A right pyramid on a base 4 cm square has a slanted edge of 6 cm. Calculate the volume of the pyramid.
  • Right-angled triangle base
    prism_rt Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
  • The quadrilateral pyramid
    jehlan_4b_obdelnik The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
  • Hexagonal pyramid
    jehlan Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
  • Tetrahedral pyramid
    jehlan Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
  • Quadrangular prism
    hranol The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
  • Triangular pyramid
    trojboky_ihlan Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
  • The pyramid 4s
    jehlan_4b_obdelnik The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of length 13 dm. Calculate the surface area and volume of this pyramid.
  • Quadrilateral pyramid
    jehlan We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid