Triangular pyramid

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

Correct result:

V =  1848.4228 cm³
S =  1179.4357 cm²

Solution:

$$\begin{gathered} a=20\text{ cm } \\ b=35\text{ cm } \\ {a}_2=a\mathrm{/}2=20\mathrm{/}2=10\text{ cm } \\ {h}_1=\sqrt{b^2-a_2^2}=\sqrt{35^2-10^2}=15\sqrt{5}\text{ cm}\doteq 33.541\text{ cm } \\ h=\sqrt{h_1^2-a_2^2}=\sqrt{33.541^2-10^2}=5\sqrt{41}\text{ cm}\doteq 32.0156\text{ cm } \\ {S}_1=a\cdot h_1\mathrm{/}2=20\cdot 33.541\mathrm{/}2=150\sqrt{5}{\text{cm}}^2\doteq 335.4102{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 20^2=100\sqrt{3}{\text{cm}}^2\doteq 173.2051{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S_2\cdot h={\displaystyle \frac{1}{3}}\cdot 173.2051\cdot 32.0156=1848.4228{\text{cm}}^3 \end{gathered}$$

$S=3\cdot S_1+S_2=3\cdot 335.4102+173.2051=1179.4357{\text{cm}}^2$

Try another example

Showing 0 comments:

Related math problems and questions:

• Triangular pyramid
  Calculate the volume and surface area of a regular triangular pyramid with height equal to the base edge 10 cm length.
• Triangular pyramid
  Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.
• Triangular pyramid
  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)?
• 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.
• Regular quadrilateral pyramid
  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.
• Pyramid height
  Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
• 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.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Pyramid 4sides
  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.
• Pentagonal pyramid
  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.
• 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.
• Runcated pyramid teapot
  The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
• 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.
• Hexagonal pyramid
  Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.
• Pyramid
  Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
• Quadrangular prism
  Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
• Pyramid a+h
  Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.