Irregular hexagon

There is an irregular hexagon whose sides are the same length. The opposite sides are parallel; their distance is 237, 195, and 193. What is its area?

Correct answer:

S =  89590.8868

Step-by-step explanation:

a1​=a2​=…=a6​=a a1​∣∣a4​ a2​∣∣a5​ a3​∣∣a6​  h1​=d(a1​,a4​) h2​=d(a2​,a5​) h3​=d(a3​,a6​)  h1​=237 h2​=195 h3​=193  s=31​⋅ (h1​+h2​+h3​)=31​⋅ (237+195+193)=3625​=20831​≐208.3333 S1​=s⋅ (s−h1​)⋅ (s−h2​)⋅ (s−h3​)​=208.3333⋅ (208.3333−237)⋅ (208.3333−195)⋅ (208.3333−193)​≐49150.556 a=3h1​⋅ h2​⋅ h3​​=3237⋅ 195⋅ 193​≐207.3863  S1​=a⋅ h1​=207.3863⋅ 237≐49150.556 S2​=a⋅ h2​=207.3863⋅ 195≐40440.3309  S=S1​+S2​=49150.556+40440.3309=89590.8868

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Showing 1 comment:
Math student
There is an irregular hexagon whose sides are the same length.
If  a1=a2=a3=a4=a5=a6 it is regular hexagon.
There is an irregular hexagon whose opposite sides are the same length....
Then is a=87,18... b=135,68... c=137,99... d=360,84...
Area of hexagons is:
S=Sd-Sa-Sb-Sc  =36875,1 (Sd; Sa; Sb; Sc is area of  equilateral triangels).





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