Bangun Ruang Sisi Datar [Part 3] - Prisma

Main ideas / lessons

• Purpose of the video: After watching, students should be able to:
  • Define prisms
  • Create prism nets
  • Determine surface area of prisms
  • Determine volume of prisms

Definition of a prism

A prism is a flat-sided 3D shape where the base and the lid are:

• Exactly the same
• Positioned so that corresponding vertices are connected by vertical lateral faces

The lateral faces form “side walls” in the shape of the base’s edges, with height measured vertically.

• The base/lid can be any flat 2D shape (e.g., square/rectangle, triangle, pentagon, etc.).
• A prism is named according to the base shape, for example:
  • Triangle base → triangular prism
  • Pentagon base → pentagonal prism
  • Rhombus base → rhombus prism

Key prism terms

• Height of the prism: the distance between the base and the lid (denoted by a symbol like t / “teh kecil”).
• Vertical sides (lateral faces): determined by the number of sides of the base.
• Net of a prism: an opened 2D layout of its faces (an example discussed: triangular prism net).

Elements of prisms (depend on the base)

For an n-sided base prism, the video states:

• Number of sides (faces): ( n + 2 )
• Number of edges: ( 3n )
• Number of vertex (corner) points: ( 2n )
• Number of vertical (lateral) sides / faces: ( n )

Example: triangular prism ((n=3))

• Faces: ( 3 + 2 = 5 )
• Edges: ( 3 \times 3 = 9 )
• Vertices: ( 2 \times 3 = 6 )
• Vertical faces: ( 3 )

Methodology / formulas for surface area and volume

1) Surface area of a prism

• Meaning: total area covering all faces of the prism.

Manual approach described:

• Compute area of base
• Add area of lid (same as base)
• Add area of all vertical lateral faces

Formula presented: [ L = 2 \cdot A_{\text{base}} + K \cdot t ] Where:

• ( L ) = surface area
• ( A_{\text{base}} ) (denoted as ela-ela in subtitles) = area of the base
• ( K ) = circumference/perimeter of the base
• ( t ) = height of the prism

2) Volume of a prism

Formula given: [ V = A_{\text{base}} \cdot t ]

Interpretation stated: Volume = “contents/capacity” = base area times prism height.

Worked example calculations (as shown)

Example 1: Right triangular prism (surface area)

Given:

• Prism height ( t = 8 )
• Right triangle base legs (3) and (4)

Steps:

• Base area: [ A = \frac{3 \times 4}{2} = 6 ]

• Perimeter of base:

  • Hypotenuse via Pythagoras: [ = 5 ]

  • ( K = 3 + 4 + 5 = 12 )

  • Surface area: [ L = 2A + Kt = 2(6) + 12(8) = 12 + 96 = 180 ]

Result: ( L = 180 \,\text{cm}^2 )

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Example 2: Isosceles trapezoidal prism (surface area)

Given (from subtitles):

• Parallel sides: (6) and (14)
• Trapezoid height (= 15) (interpreted as prism height (t))
• Other side lengths used (including a right-triangle/Pythagorean step) to obtain the final perimeter

Steps (as presented):

• Base area: [ A = \frac{(6+14)\cdot 3}{2} = \frac{20 \cdot 3}{2} = 30 ]

• Perimeter of base:

  • Final perimeter used: ( K = 30 ) (subtitles were noted as error-prone; the intended perimeter value is stated as (K=30))

• Surface area: [ L = 2(30) + 30(15) = 60 + 450 = 510 ]

Result: ( L = 510 \,\text{cm}^2 )

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Example 3: Rhombus prism (find height from surface area)

Given:

• Surface area ( L = 672 \,\text{cm}^2 )
• Rhombus diagonals: (16) and (12)

Steps:

• Base area (rhombus): [ A = \frac{d_1 d_2}{2} = \frac{16 \cdot 12}{2} = 96 ]

• Perimeter:

  • Half-diagonals: (8) and (6)

  • Side length: [ \sqrt{8^2 + 6^2} = 10 ]

  • ( K = 10+10+10+10 = 40 )

  • Use surface area formula: [ 672 = 2(96) + 40t = 192 + 40t ] [ 40t = 672 - 192 = 480 \Rightarrow t = 12 ]

Result: prism height ( t = 12 \,\text{cm} )

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Example 4: Rhombus prism (volume)

Given:

• Rhombus diagonals: (16) and (20)
• Prism height ( t = 24 )

Steps:

• Base area: [ A = \frac{16 \cdot 20}{2} = 160 ]

• Volume: [ V = A \cdot t = 160 \cdot 24 = 3840 ]

Result: ( V = 3840 \,\text{cm}^3 )

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Example 5: Triangular prism shaped tent (find tent height)

Given:

• Prism length/height parameter: ( t = 4 ) meters
• Volume: ( V = 10 \,\text{m}^3 )
• Triangle base uses a side labeled base (= 2.5)

Steps:

• Triangle area: [ A = \frac{(2.5)\cdot h}{2} ]

• Volume: [ 10 = A \cdot 4 ] [ 10 = 5h \Rightarrow h = 2 ]

Result: tent height ( h = 2 \,\text{meters} )

“Your turn” activity

• The video ends with an instruction:
  • Students solve the next question themselves
  • Then write the answer in the comments
  • Later check with an answer key (mentioned as provided in the video description with “B is placed in the description”)

Speakers / sources featured

• Mr. Beni (main instructor/speaker)