Triangular prism - regular

The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.


V =  36.373 cm3
S =  83.138 cm2


v=3 cm h=7 cm  a2=v2+(a/2)2 4a2=4v2+a2 3a2=4v2  a=v 2/3=3 2/32 3 cm3.4641 cm  S1=34 a2=34 3.464123 3 cm25.1962 cm2  V=S1 h=5.1962 721 336.373136.373 cm3v=3 \ \text{cm} \ \\ h=7 \ \text{cm} \ \\ \ \\ a^2=v^2 + (a/2)^2 \ \\ 4a^2=4v^2 + a^2 \ \\ 3a^2=4v^2 \ \\ \ \\ a=v \cdot \ 2/\sqrt{ 3 }=3 \cdot \ 2/\sqrt{ 3 } \doteq 2 \ \sqrt{ 3 } \ \text{cm} \doteq 3.4641 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 3.4641^2 \doteq 3 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 5.1962 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=5.1962 \cdot \ 7 \doteq 21 \ \sqrt{ 3 } \doteq 36.3731 \doteq 36.373 \ \text{cm}^3
o=3 a=3 3.46416 3 cm10.3923 cm  S=2 S1+o h=2 5.1962+10.3923 748 383.138483.138 cm2o=3 \cdot \ a=3 \cdot \ 3.4641 \doteq 6 \ \sqrt{ 3 } \ \text{cm} \doteq 10.3923 \ \text{cm} \ \\ \ \\ S=2 \cdot \ S_{1} + o \cdot \ h=2 \cdot \ 5.1962 + 10.3923 \cdot \ 7 \doteq 48 \ \sqrt{ 3 } \doteq 83.1384 \doteq 83.138 \ \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 1 comment:
Hola Qomo Estas
hola qomo estas ya se que esta mal escrito


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:

  1. 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.
  2. Triangular prism,
    prism3s The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).
  3. Prism
    prism The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
  4. 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.
  5. Triangular pyramid
    3sidesPyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
  6. Base of prism
    hranol3b The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
  7. 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
  8. Embankment
    nasyp The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
  9. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  10. Wall height
    jehlan_2 Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
  11. Quadrangular pyramid
    jehlan_4b_obdelnik_1 Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
  12. Tetrahedral pyramid
    jehlan_4b_obdelnik_3 Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
  13. Horses playground
    kone_dzokej The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
  14. Cone container
    kuzel_1 Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
  15. RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  16. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  17. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?