Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.

Correct result:

S =  524 cm²
V =  720 cm³

Solution:

$$\begin{gathered} a=12\text{ cm } \\ b=7\text{ cm } \\ v=6\text{ cm } \\ h=10\text{ cm } \\ {S}_1=a\cdot v=12\cdot 6=72{\text{cm}}^2 \\ {S}_2=h\cdot (2\cdot a+2\cdot b)=10\cdot (2\cdot 12+2\cdot 7)=380{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 72+380=524{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h=72\cdot 10=720{\text{cm}}^3$

Try another example

Showing 0 comments:

Related math problems and questions:

• Tetrahedral prism - rhomboid base
  Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
• Prism
  Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
• Quadrangular prism
  The quadrangular prism has a volume of 648 cm³. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
• 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.
• Quadrilateral pyramid
  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.
• 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.
• 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.
• Prism height
  What is the height of the prism with the base of a right triangle with 6 cm and 9 cm? The diaphragm is 10.8 cm long. The volume of the prism is 58 cm³. Calculate its surface.
• 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
• Quadrangular prism
  The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the 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.
• 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
• Square prism
  Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
• 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.
• 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.
• Trapezoidal prism
  Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm. L