Triangular prism - regular

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.

Correct answer:

V =  36.3731 cm³
S =  83.1384 cm²

Step-by-step explanation:

$$\begin{gathered} v=3\text{ cm } \\ h=7\text{ cm } \\ {a}^2=v^2+(a\mathrm{/}2{)}^2 \\ 4a^2=4v^2+a^2 \\ 3a^2=4v^2 \\ a=v\cdot 2\mathrm{/}\sqrt{3}=3\cdot 2\mathrm{/}\sqrt{3}=2\sqrt{3}\text{ cm}\doteq 3.4641\text{ cm } \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 3.4641^2=3\sqrt{3}{\text{cm}}^2\doteq 5.1962{\text{cm}}^2 \\ V=S_1\cdot h=5.1962\cdot 7=21\sqrt{3}=36.3731{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=3\cdot a=3\cdot 3.4641=6\sqrt{3}\text{ cm}\doteq 10.3923\text{ cm } \\ S=2\cdot S_1+o\cdot h=2\cdot 5.1962+10.3923\cdot 7=48\sqrt{3}=83.1384{\text{cm}}^2 \end{gathered}$$

Try calculation via our triangle calculator.

Try another example

Showing 1 comment:

Hola Qomo Estas

hola qomo estas ya se que esta mal escrito

11 months ago  Like

Related math problems and questions:

• Triangular prism,
  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).
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
• 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.
• 3sides prism
  The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
• Base of prism
  The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
• 3s prism
  It is given a regular perpendicular triangular prism with a height of 19.0 cm and a base edge of 7.1 cm. Calculate the volume of the prism.
• Triangular prism
  The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
• 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)?
• 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.
• Prism
  The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
• 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.
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• Triangular pyramid
  A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
• 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.
• Rhombus base
  Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 15 cm. Prism height is twice the base edge length.
• Isosceles + prism
  Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm
• Quadrangular prism
  Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.