In ΔABC, AD and CE are the two medians drawn from A and C respectively, meeting BC and AB at D and E respectivley. AD and CE intersect at O. DF is drawn parallel to CE and meets AB at F. If area of ΔCOD is 16 cm2, what is the area of quadrilateral DOEF?
Explanation:
We know centroid (O) divides the bigger triangle in 6 smaller triangles of equal areas.
∴ Area of ΔABC = 6 × (Area of ΔCOD) = 6 × 16 = 96 cm2.
Area of ΔBEC = 1/2 of ΔABC = 1/2 of 96 = 48 cm2.
Now, ΔBFD is similar to ΔBEC
∴ Area of ΔBFD : Area of ΔBEC = BD2 : BC2 = 1 : 4
⇒ Area of ΔBFD = 48/4 = 12 cm2.
Now, Area of DOEF = Area of ΔBEC - Area of ΔBFD - Area of ΔCOD = 48 - 12 - 16 = 20 cm2.
Hence, option (c).
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