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.

Correct answer:

V =  300 cm³

Step-by-step explanation:

$$\begin{gathered} a=5\text{ cm } \\ h=10\text{ cm } \\ S=130{\text{cm}}^2 \\ c=S\mathrm{/}h=130\mathrm{/}10=13\text{ cm } \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12\text{ cm } \\ {S}_2=a\cdot b\mathrm{/}2=5\cdot 12\mathrm{/}2=30{\text{cm}}^2 \\ V=S_2\cdot h=30\cdot 10=300{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Triangular prism
  The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the prism's largest wall is 130 cm², and the body height is 10 cm. Calculate the body 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.
• 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.
• 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
• 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?
• Triangular pyramid
  Calculate the volume and surface area of a regular triangular pyramid with height equal to the base edge 10 cm length.
• 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.
• 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.
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• 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
• Triangular prism
  Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm, and height of prism h=12 cm.
• 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
  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
  Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
• Regular triangular prism
  Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
• 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.
• Right-angled triangle base
  Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.