In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB respectively of ABC. Prove that BCEF is a trapezium and area of trap. BCEF = 3/4 area of ABC.
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Area of BCEF = (3/4) Area of Δ ABC
Step-by-step explanation:
D, E and F are mid-points of the sides BC, CA and AB
=> AF / BF = AE / CE
=> FE || BC
=> BCEF is a trapezium
Δ AFE ≈ Δ ABC
AF/AB = 1/2
=> Area of ΔAFE = (1/2)² Area of Δ ABC
=> Area of ΔAFE = (1/4) Area of Δ ABC
Area of BCEF = Area of Δ ABC - Area of ΔAFE
=> Area of BCEF = Area of Δ ABC - (1/4) Area of Δ ABC
=> Area of BCEF = (3/4) Area of Δ ABC
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