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प्रश्न
In the given figure, AD // BE // CF.
Prove that area (ΔAEC) = area (ΔDBF)
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उत्तर
We know that the area of triangles on the same base and between the same parallel lines are equal.
Consider ABED quadrilateral; AD || BE.
With the common base, BE and between AD and BE parallel lines, we have
Area of ΔABE = Area of ΔBDE
Similarly, in BEFC quadrilateral, BE || CF
With common base BC and between BE and CF parallel lines, we have
Area of ΔBEC = Area of ΔBEF
Adding both equations, we have
Area of ΔABE + Area of ΔBEC = Area of ΔBEF + Area of ΔBDE
⇒ Area of AEC = Area of DBF
Hence Proved.
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संबंधित प्रश्न
In the given figure, if the area of triangle ADE is 60 cm2, state, given reason, the area of :
(i) Parallelogram ABED;
(ii) Rectangle ABCF;
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(iii) Length of altitude from A on CD;
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find the area of the parallelogram ABCD.
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(iii) also, find the area of parallelogram ABCD.
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