Created by: Olivia Mouriopoulos and Karim Farkhad
Legend: black font=Olivia's work, blue font=Karim's work

Prisms


Prisms:
  • a solid having bases or ends that are parallel, congruent polygons and sides that parallelograms.
  • a form having faces parallel to the vertical axis and intersecting the horizontal axis
  • a transparent solid body, often having triangular bases, used for dispersing light into a spectrum or for reflecting rays of light
  • are polyhedrons,coming in multiple different forms with various faces,vertices and edges
There are specific formulas to find the volume or surface area of a 3-D shape or just area or perimeter of a 2-D shape, but when dealing with prisms we only use 3-D shapes. These formulas differ for each prism.
Remember these formulas are for standardized prisms only and will work only with them. Certain prisms have odd faces, and may have different dimensions for each and every edge/face
legend.jpg




>
  • For a...
  • Rectangular Prism*Note: A cube is also a rectangular prism.*
  • cube.gif
  • Width=2cm, height=4cm, length=2cm
  • SURFACE AREA
  • A=2(wh+lw+lh)
  • A=2(2x4+2x2+2x4)
  • A=2(8+4+8)
  • A=2(20)
  • A=40cm²
  • VOLUME
  • V=lwh
  • V=(2)(4)(2)
  • V=16cm³

  • For a ...

  • Triangular Prism
  • triangular-prism.png
  • height=4cm, width/base=4cm, length=4cm, slant height=4cm
  • SURFACE AREA

  • ATriangle=bh/2(formula)
  • Atriangle=4(4)/2
  • Atriangle=8cm²
  • Arectangle= lw(formula)
  • Arectangle=4(4)
  • Arectangle=16cm²
  • SA=(2)Atriangle+(3)Arectangle(formula)
  • SA=(2)(8)+(3)(16)
  • SA= 16+3(16)
  • SA=16+48
  • SA=64cm^2

  • Volume
  • V=bhl/2
  • V= (4)(4)(4)/2
  • V=(16)(4)/2
  • V=(64)/2
  • V=32cm³

>
  • For a...

  • Pentagonal Prism(standard)
  • prism.gif
  • Surface Area

  • Example: s=4,h=4,a=4(a is the median from a vertex opposite another)

  • ABase= (A)(5)(S)/2
  • ABase= (4)(5)(4)/2
  • ABase= (20)(4)/2
  • ABase= (80)/2
  • ABase= 40cm²

  • Atriangle=(S)(H)
  • Atriangle=(4)(4)
  • Atriangle=16cm²

  • SA=(2)Abase +5(Arectangle)
  • SA=(2)(40)+5(16)
  • SA=80+80
  • SA= 160cm²SA=(2)Abase +5(Arectangle)

  • Volume
  • V=(5/2)ash
  • V=5/2(4)(4)(4)
  • V=2.5(4)(4)(4)
  • V=10(4)(4)
  • V=(40)(4)
  • V=160cm³
_
Now for a...
Hexagonal Prism


hexa.jpg
SA=(2)Abase+(6)Arectangle
Example: s=4,a=4,h
=4
Abase= (4)(6)(4)/2
Abase= 24(4)/2
Abase= 96/2
Abase= 48cm²

Atriangle=
lw
Atriangle=(4)(4)
Atriangle=16cm²

SA=(2)Abase+(6)Arectangle
SA=(2)(48)+(6)(16)
SA=96+(6)(16)
SA=96+96
SA=192cm ²

Volume=
3ash
V=(3)(4)(4)(4)

V=12(4)(4)
V=48(4)
V=192cm
³__

Be sure to remember that these formulas are only for standardized shapes and certain polyhedrons can have unusually shaped edges.