Hexagonal 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.

Correct result:

S =  674.261 cm2


r=8 cm a=r=8 cm h=20 cm S1=3 3/2 a2=3 3/2 8296 3 cm2166.2769 cm2  a2=3/2 a=3/2 84 3 cm6.9282 cm h2=a22+h2=6.92822+2028 7 cm21.166 cm  S2=a h2/2=8 21.166/232 7 cm284.664 cm2  S=S1+6 S2=166.2769+6 84.664=674.261 cm2r=8 \ \text{cm} \ \\ a=r=8 \ \text{cm} \ \\ h=20 \ \text{cm} \ \\ S_{1}=3 \cdot \ \sqrt{ 3 }/2 \cdot \ a^2=3 \cdot \ \sqrt{ 3 }/2 \cdot \ 8^2 \doteq 96 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 166.2769 \ \text{cm}^2 \ \\ \ \\ a_{2}=\sqrt{ 3 }/2 \cdot \ a=\sqrt{ 3 }/2 \cdot \ 8 \doteq 4 \ \sqrt{ 3 } \ \text{cm} \doteq 6.9282 \ \text{cm} \ \\ h_{2}=\sqrt{ a_{2}^2+h^2 }=\sqrt{ 6.9282^2+20^2 } \doteq 8 \ \sqrt{ 7 } \ \text{cm} \doteq 21.166 \ \text{cm} \ \\ \ \\ S_{2}=a \cdot \ h_{2}/2=8 \cdot \ 21.166/2 \doteq 32 \ \sqrt{ 7 } \ \text{cm}^2 \doteq 84.664 \ \text{cm}^2 \ \\ \ \\ S=S_{1}+6 \cdot \ S_{2}=166.2769+6 \cdot \ 84.664=674.261 \ \text{cm}^2

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!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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

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.
  • The tent
    stan Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.
  • Quadrilateral pyramid
    ihlan_rez In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area.
  • Quadrilateral pyramid
    jehlan_4b_obdelnik Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 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.
  • Tetrahedral pyramid
    ihlan Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
  • Quadrilateral prism
    cuboid The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
  • Pentagonal prism
    penta-prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
  • Triangular prism
    hranol3b_1 Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
  • Triangular prism - regular
    prism3s 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.
  • Triangular prism
    hranol3b The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
  • Triangular prism
    prism3 Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.
  • 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).
  • Two hemispheres
    hemisphere3 In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?
  • Two bodies
    cylinders The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
  • The hollow cylinder
    duty_valec The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity?
  • Wallpaper
    net of cube 3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?