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geom3d

 area
 compute the area of a triangle, or the surface area of a sphere or a regular polyhedron

 Calling Sequence area(obj)

Parameters

 obj - triangle, sphere, or regular polyhedron

Description

 • The routine area returns the area or surface area of the input object which is a triangle, a sphere, or a regular polyhedron.
 • The command with(geom3d,area) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Define triangle ABC with vertices A, B and C

 > $\mathrm{triangle}\left(\mathrm{ABC},\left[\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,2,0,0\right),\mathrm{point}\left(C,1,3,0\right)\right]\right):$

Find the area of ABC

 > $\mathrm{area}\left(\mathrm{ABC}\right)$
 ${3}$ (1)

Define an icosahedron with center o(1,2,5) and the radius of the circum-sphere is 1

 > $\mathrm{icosahedron}\left(\mathrm{ico},\mathrm{point}\left(o,1,2,5\right),1\right)$
 ${\mathrm{ico}}$ (2)

Find the surface area of ico

 > $\mathrm{area}\left(\mathrm{ico}\right)$
 $\frac{{4}{}\sqrt{{3}}{}\sqrt{{5}}}{\frac{{1}}{{2}}{+}\frac{{1}}{{2}}{}\sqrt{{5}}}$ (3)
 > $\mathrm{draw}\left(\mathrm{ico},\mathrm{style}=\mathrm{patch},\mathrm{lightmodel}=\mathrm{light4},\mathrm{orientation}=\left[-136,56\right],\mathrm{title}='\mathrm{icosahedron}'\right)$