in triangle abc d and e are points on ab and ac respectively f is the point on bc. df is parallel to ac and ef is parallel to ab the area of triangle efc and abc is 64 and 400 respectively. find the area of the quadrilateral adfe
Answers
Given : in triangle abc , d and e are points on ab and ac respectively . f is the point on bc. df || ac and ef || ab the area of triangle efc = 64 & abc = 400
To find: the area of the quadrilateral adfe
Solution:
ef ║ab
=> Δefc ≈ Δabc
=> (fc/bc )² = Area of Δefc / Area of Δabc
=> (cf/bc )² = 64/400
=> cf/bc = 8/20
=> cf/bc = 2/5
bf = bc - cf
=> bf = bc - 2bc/5
=> bf = 3bc/5
=> bf/bc = 3/5
df ║ ac
=> Δbfd ≈ Δ bca
=> (bf/bc )² = area of Δ bfd / area of Δ bca
=> (3/5)² = area of Δ bfd / 400
=> 9/25 = area of Δ bfd / 400
=> area of Δ bfd = 144
area of the quadrilateral adfe = area of Δabc - Area of Δefc - Area of Δbfd
= 400 - 64 - 144
= 400 - 208
= 192
area of the quadrilateral adfe = 192 sq units
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