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.

Correct answer:

S =  1416 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{ cm } \\ r=13\text{ cm } \\ h=\sqrt{r^2-(a\mathrm{/}2{)}^2}=\sqrt{13^2-(10\mathrm{/}2{)}^2}=12\text{ cm } \\ {S}_1=a\cdot h\mathrm{/}2=10\cdot 12\mathrm{/}2=60{\text{cm}}^2 \\ {S}_2=(2\cdot r+a)\cdot 3\cdot h=(2\cdot 13+10)\cdot 3\cdot 12=1296{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 60+1296=1416{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• 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
• Total area
  Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height is 10 cm.
• Prism height
  What is the prism's height with the base of a right triangle of 6 cm and 9 cm? The diaphragm is 10.8 cm long. The volume of the prism is 58 cm³. Calculate its surface.
• 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
• 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.
• 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.
• 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.
• 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'
• 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.
• Cone and the ratio
  The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.
• 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
• Arm and base
  The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
• 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.
• 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.
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.
• Isosceles trapezoid
  Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• Base of an isosceles triangle
  Calculate the size of the base of an isosceles triangle, the height is 5 cm and the length of the arm is 6.5 cm. What is the perimeter of this triangle?