answer the above question
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Answer:81
Answer is long, read carefully
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In the diagram
Three triangles are similar
ΔODF∽ΔGHO∽ΔEOI *AA similarity*
Also
ΔODF:ΔGHO:ΔEOI=2²:3²:4²
Ratio of similarity is
2:3:4
Also they are similar to ΔABC
In the line BC
BC=BD+DF+CF
*HO=BD* (BDOH is a parallelogram)
*OI=FC* (CFOI is a parallelogram)
→BC=HO+DF+OI
→BC:HO:DF:OI=(2+3+4):2:3:4
Finally the ratio of similarity is
9:2:3:4
The ratio of area is
ΔABC:ΔODF:ΔGHO:ΔEOI=9²:2²:3²:4²
FINAL ANSWER
The area of ΔABC is 81.
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