Pentagonal pyramid

Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.

Correct answer:

V =  3016.1483 cm3
S =  1347.0581 cm2

Step-by-step explanation:

a=12.8 cm v=32.1 cm n=5  S1=14 5 (5+2 5) a2=14 5 (5+2 5) 12.82281.883 cm2  V=13 S1 v=13 281.883 32.1=3016.1483 cm3
S1=n A T=S1/n=281.883/556.3766 cm2  T=a h12  h1=2 Ta=2 56.376612.88.8088 cm  h22=v2+h12  h2=v2+h12=32.12+8.8088233.2867 cm  S2=a h22=12.8 33.28672213.035 cm2  S=S1+n S2=281.883+5 213.035=1347.0581 cm2



We will be pleased if You send us any improvements to this math problem. Thank you!






Showing 2 comments:
#
Sebf
Perfect!
Thanks for demonstration
Really thanks
Sébastien

#
Sebf
I think we should see all the variables, I mean : a, v, n S1, S2 and all the things used to finally get the result S. On the scheme.
I understand the way you calculate on your savant literature. But I 'm sure i' m not the only one who would like to learn about this science visually.
For me it's OK. But I cannot share that.
Very sad while it is very clever.
Please explain how you get the result visually on the scheme.

Thanks by advance

Regards

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.

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

Related math problems and questions:

  • Pentagonal pyramid
    pentagon_1 The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
  • Hexagonal pyramid
    hexa_pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
  • 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.
  • 9-gon pyramid
    9gon+Base+cone Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
  • Hexagonal pyramid
    hex_pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
  • Pyramid 4sides
    pyramid_2 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.
  • Hexagon cut pyramid
    pravkomoly Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
  • Wall height
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
  • Hexagonal pyramid
    hexa_pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
  • Regular quadrilateral pyramid
    ihlan_rez What is the volume of a regular quadrilateral pyramid if its surface is 576 cm2 and the base edge is 16 cm?
  • Truncated pyramid
    truncated_pyramid Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
  • Quadrilateral pyramid,
    jehlan_4b_obdelnik A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
  • Regular quadrilateral pyramid
    pyramid_3 Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
  • Quadrangular pyramid
    pyramid_4s_1 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
    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)?
  • 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
  • Find the
    ihlan Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm3 and a height of 45 cm.