Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?

Correct answer:

S =  828.4

Step-by-step explanation:

$$\begin{gathered} a=16 \\ v=16 \\ {w}_1=\sqrt{v^2+({\displaystyle \frac{a}{2}}{)}^2}=\sqrt{16^2+({\displaystyle \frac{16}{2}}{)}^2}=8\sqrt{5}\doteq 17.8885 \\ {S}_1=a^2=16^2=256 \\ {S}_2={\displaystyle \frac{a\cdot w_1}{2}}={\displaystyle \frac{16\cdot 17.8885}{2}}=64\sqrt{5}\doteq 143.1084 \\ S=S_1+4\cdot S_2=256+4\cdot 143.1084=828.4 \end{gathered}$$

Try another example

Related math problems and questions:

• 4s pyramid
  Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
• 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?
• Regular 4-sided pyramid
  Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.
• Tetrahedral pyramid
  Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm², and the deviation angle of the side edges from the plane of the base is 60 degrees.
• Quadrilateral pyramid
  Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.
• Hexagonal pyramid
  Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• Pyramid roof
  2/4 of the area of ​​the roof-shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?
• 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.
• 4side pyramid
  Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if the edge of the base is 8 cm long and the height of the side wall is 5 cm?
• Tetrahedral pyramid
  Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
• Pyramid four sides
  In a regular tetrahedral pyramid is a body height of 38 cm and a wall height of 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
• 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.
• Quadrilateral pyramid
  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.
• Base diagonal
  In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
• Quadrilateral pyramid
  We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
• Tetrahedral pyramid
  It is given a regular tetrahedral pyramid with a base edge of 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.