Vertical prism

The base of 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

Correct result:

S =  960 cm²
V =  900 cm³

Solution:

$$\begin{gathered} a=5 \\ c=13 \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12 \\ h=a+b+c=5+12+13=30 \\ P=a\cdot b\mathrm{/}2=5\cdot 12\mathrm{/}2=30 \\ S=2\cdot P+a\cdot h+b\cdot h+c\cdot h=2\cdot 30+5\cdot 30+12\cdot 30+13\cdot 30=960{\text{cm}}^2 \end{gathered}$$

$V=P\cdot h=30\cdot 30=900{\text{cm}}^3$

Try another example

Showing 0 comments:

Next similar math problems:

• Center traverse
  It is true that the middle traverse bisects the triangle?
• Double ladder
  The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
• Double ladder
  The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
• Isosceles III
  The base of the isosceles triangle is 17 cm area 416 cm². Calculate the perimeter of this triangle.
• 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.
• Cone
  Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
• Embankment
  The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m³ of soil is in the embankment?
• 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
• ISO Triangle V2
  Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
• 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.
• Triangular prism
  Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)
• Prism
  Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
• Triangular prism
  The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm² and the body height is 10 cm. Calculate the body volume.
• 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.
• 3s prism
  It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
• Rhombus base
  Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 10 cm. Prism height is twice base edge length.
• Triangular prism
  Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.