In the diagram below, CD = BF = 10 units and ∠CED = ∠BAF = 30°. What would be the area of triangle AED? (Note: Diagram below may not be proportional to scale.)
Explanation:
m∠ECD = m∠BCF = 60° Also, m∠AFB = 60°, m∠BFC = 30° ∴ m∠AFC = 90° In a 30° - 60° - 90° triangle, sides are in the ratio 1:3:2.
So, in ∆EDC, ED = 10√3 units
Also, in ∆FBC, BF = 10 units
⇒FC=203 units and BC = 103
In ∆AFC,
FC=203 units⇒AC=403 units
∴AD=10+403 units
A(∆ADE)=12×103×10+403
= 50(√3 + 4) sq.units
Hence, option (d).
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