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. Find the volume and surface of the prism.

Correct answer:

V =  1870.6149 cm³
S =  1108.2459 cm²

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ h=5\text{ cm } \\ o=6\cdot a=6\cdot 12=72\text{ cm } \\ v=\sqrt{a^2-(a\mathrm{/}2{)}^2}=\sqrt{12^2-(12\mathrm{/}2{)}^2}=6\sqrt{3}\text{ cm}\doteq 10.3923\text{ cm } \\ {S}_1=a\cdot v\mathrm{/}2=12\cdot 10.3923\mathrm{/}2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_6=6\cdot S_1=6\cdot 62.3538=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ V=S_6\cdot h=374.123\cdot 5=1870.6149{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_6+o\cdot h=2\cdot 374.123+72\cdot 5=1108.2459{\text{cm}}^2$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• Hexagon
  Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm.
• 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.
• Hexa prism
  Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
• Hexagonal pyramid
  Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
• Regular hexagonal pyramid
  Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
• Triangular prism
  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.
• Prism - eq triangle
  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.
• 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.
• Vertical prism
  The base of the 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
• Triangular prism
  The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The content area of the largest sidewall of its surface is 130 cm², and the height of the body is 10 cm. Calculate its volume.
• Triangular prism
  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.
• Hexagonal prism
  Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm.
• Triangular prism
  Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm.
• The regular
  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.
• Triangular prism
  Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
• Hexagonal 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 prism 2
  The regular hexagonal prism has a surface of 140 cm² and height of 5 cm. Calculate its volume.