3-D+Shapes+-+Prisms

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

=Prisms=

Prisms: 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 __
 * 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
 * 

> > **For a...** > __**Rectangular Prism**__***Note: A cube is also a rectangular prism.*** > > **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=40cm ² >  > **__VOLUME __** > V=lwh > V=(2)(4)(2) > <span style="color: rgb(0, 0, 0);">V=16cm ³

> **For a ...** > > **__Triangular Prism__** > > **height=4cm, width/base=4cm, length=4cm, slant height=4cm** > **__SURFACE AREA__** > > <span style="color: rgb(0, 0, 255);">**A**Triangle=bh/2(formula) > <span style="color: rgb(0, 0, 255);">**A**triangle=4(4)/2 > <span style="color: rgb(0, 0, 255);">__**A**triangle=8cm__² > <span style="color: rgb(0, 0, 255);"> > <span style="color: rgb(0, 0, 255);">**A**rectangle= lw(formula) > <span style="color: rgb(0, 0, 255);">**A**rectangle=4(4) > <span style="color: rgb(0, 0, 255);">__**A**rectangle=16cm__² > <span style="color: rgb(0, 0, 255);"> > <span style="color: rgb(0, 0, 255);">SA=(2)Atriangle+(3)Arectangle(formula) > <span style="color: rgb(0, 0, 255);">SA=(2)(8)+(3)(16) > <span style="color: rgb(0, 0, 255);">SA= 16+3(16) > <span style="color: rgb(0, 0, 255);">SA=16+48 > <span style="color: rgb(0, 0, 255);">__SA=64cm^2__ > > __**Volume**__ > <span style="color: rgb(0, 0, 255);">V=bhl/2 > <span style="color: rgb(0, 0, 255);">V= (4)(4)(4)/2 > <span style="color: rgb(0, 0, 255);">V=(16)(4)/2 > <span style="color: rgb(0, 0, 255);">V=(64)/2 > __<span style="color: rgb(0, 0, 255);">V=32cm//³// __

> > **For a...** > > __**Pentagonal Prism(standard)**__ > > __Surface Area__ > > <span style="color: rgb(0, 0, 255);">Example: s=4,h=4,a=4(a is the median from a vertex opposite another) > <span style="color: rgb(0, 0, 255);"> > > <span style="color: rgb(0, 0, 255);"> > <span style="color: rgb(0, 0, 255);">ABase= (A)(5)(S)/2 > <span style="color: rgb(0, 0, 255);">ABase= (4)(5)(4)/2 > <span style="color: rgb(0, 0, 255);">ABase= (20)(4)/2 > <span style="color: rgb(0, 0, 255);">ABase= (80)/2 > <span style="color: rgb(0, 0, 255);">ABase= 40cm² > <span style="color: rgb(0, 0, 255);"> > > <span style="color: rgb(0, 0, 255);"> > <span style="color: rgb(0, 0, 255);">Atriangle=(S)(H) > <span style="color: rgb(0, 0, 255);">Atriangle=(4)(4) > <span style="color: rgb(0, 0, 255);">Atriangle=16cm² > <span style="color: rgb(0, 0, 255);"> > > <span style="color: rgb(0, 0, 255);"> > <span style="color: rgb(0, 0, 255);">SA=(2)Abase +5(Arectangle) > <span style="color: rgb(0, 0, 255);">SA=(2)(40)+5(16) > <span style="color: rgb(0, 0, 255);">SA=80+80 > <span style="color: rgb(0, 0, 255);">SA= 160cm²SA=(2)Abase +5(Arectangle) > <span style="color: rgb(0, 0, 0);"> > > <span style="color: rgb(0, 0, 0);"> > <span style="color: rgb(0, 0, 255);">__**<span style="color: rgb(0, 0, 0);">Volume **__ > <span style="color: rgb(0, 0, 255);"><span style="color: rgb(0, 0, 0);"> V=(5/2)ash > <span style="color: rgb(0, 0, 255);">V=5/2(4)(4)(4) > <span style="color: rgb(0, 0, 255);">V=2.5(4)(4)(4) > <span style="color: rgb(0, 0, 255);">V=10(4)(4) > <span style="color: rgb(0, 0, 255);">V=(40)(4) > <span style="color: rgb(0, 0, 255);">V=160cm __<span style="color: rgb(0, 0, 255);">//³// __ <span style="color: rgb(0, 0, 0);"> _______________________________ <span style="color: rgb(0, 0, 255);">Now for a... Hexagonal Prism

<span style="color: rgb(0, 0, 255);"> 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= 48cm<span style="color: rgb(0, 0, 255);">²

Atriangle= lw Atriangle=(4)(4) Atriangle=16cm<span style="color: rgb(0, 0, 255);">²

SA= (2)Abase+(6)Arectangle SA=(2)(48)+(6)(16) SA=96+(6)(16) SA=96+96 SA=192cm <span style="color: rgb(0, 0, 255);">²

Volume= 3ash V=(3)(4)(4)(4) V=12(4)(4) V=48(4) V=192cm__<span style="color: rgb(0, 0, 255);">//³// __

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