See complete Problem 212 at:

gogeometry.com/problem/p212_triangle_120_equilateral_area.htm

120 degrees triangle, equilateral triangle, areas. Level: High School, SAT Prep, College geometry

## Wednesday, December 24, 2008

### Elearn Geometry Problem 212: 120 Degree Triangle, Areas

Labels:
120,
area,
congruence,
equilateral,
triangle

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Sa= (root3)*a^2/4

ReplyDeleteSb= (root3)*b^2/4

Sc= (root3)*c^2/4

S= 1/2*ac*Sin 120=(root3)*ac/4

but by cosine rule

b^2=a^2+c^2+ac so ac= b^2- a^2- c^2

s=(root3)/4*ac

= (root3)/4[b^2-c^2-a^2]

= Sb-Sc-Sa

hence Sb=Sa+Sc+S -----(1)

but S^2=Sa*Sc

S= root of (Sa*Sc)

substitute in equation 1

we get Sb=Sa+Sc+ root of (Sc*Sa)

hence solved.