Mathematics
In the adjoining figure, E is the midpoint of the side AB of a triangle ABC and EBCF is a parallelogram. If the area of ∆ ABC is 25 sq. units, find the area of || gm EBCF.
Theorems on Area
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Answer
In △ABC,
As E is mid-point of AB and EF || BC so,
G is mid-point of AC (By mid-point theorem)
∴ AG = GC.
In ∆AEG and ∆CFG,
∠EAG = ∠GCF (Alternate angles are equal)
∠EGA = ∠CGF (Vertically opposite angles are equal)
AG = GC (Proved above)
Hence, ∆AEG ≅ ∆CFG (By ASA axiom)
∴ area of ∆AEG = area of ∆CFG ……….(i)
From figure,
area of || gm EBCF = area of quad. BCGE + area of ∆CFG
= area of quad. BCGE + area of ∆AEG ……..(from i)
= area of ∆ABC = 25 sq. units.
Hence, area of ||gm EBCF = 25 sq. units.
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