Hexagonal 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!

Correct result:

V =  1870.615 cm3
S =  1108.246 cm2

Solution:

a=12 cm h=5 cm o=6 a=6 12=72 cm v=a2(a/2)2=122(12/2)26 3 cm10.3923 cm S1=a v/2=12 10.3923/236 3 cm262.3538 cm2 S6=6 S1=6 62.3538216 3 cm2374.123 cm2 V=S6 h=374.123 5=1080 3=1870.615 cm3a=12 \ \text{cm} \ \\ h=5 \ \text{cm} \ \\ o=6 \cdot \ a=6 \cdot \ 12=72 \ \text{cm} \ \\ v=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 12^2-(12/2)^2 } \doteq 6 \ \sqrt{ 3 } \ \text{cm} \doteq 10.3923 \ \text{cm} \ \\ S_{1}=a \cdot \ v/2=12 \cdot \ 10.3923/2 \doteq 36 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 62.3538 \ \text{cm}^2 \ \\ S_{6}=6 \cdot \ S_{1}=6 \cdot \ 62.3538 \doteq 216 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 374.123 \ \text{cm}^2 \ \\ V=S_{6} \cdot \ h=374.123 \cdot \ 5=1080 \ \sqrt{ 3 }=1870.615 \ \text{cm}^3
S=2 S6+o h=2 374.123+72 5=1108.246 cm2S=2 \cdot \ S_{6} + o \cdot \ h=2 \cdot \ 374.123 + 72 \cdot \ 5=1108.246 \ \text{cm}^2

Try calculation via our triangle calculator.




Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  • Hexagon
    hexa_prism Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
  • 3s prism
    Prism It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
  • Octagonal tank
    octagon_prism The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
  • Hexa prism
    hexagon Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
  • Triangular prism
    hranol_3 Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
  • Vertical prism
    hranoly3 The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
  • Prism - eq triangle
    prism-3sides_1 Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
  • Prism
    hranol_3bokovy_1 Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
  • Triangular prism
    hranol_3bokovy Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
  • Triangular prism
    prism3_1 Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)
  • Triangular prism
    hranol_5 The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
  • Pyramid height
    pyramid333 Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Right angle
    triangles_1 If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  • Equilateral triangle v2
    eq_triangle Equilateral triangle has a perimeter 36 dm. What is its area?