Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is
Explanation:
BD, CE and AF are medians of the triangle ABC.
We know centroid (O) divides the triangle in 6 smaller triangles of equal area. ⇒ Area(∆EOB) = Area(∆BOF) = Area(∆FOC) = Area(∆COD) = 1/6 × 108 = 18.
∆AED ~ ∆ABC ⇒ Area(∆AED)Area(∆ABC) = AEAB2 = 14
⇒ Area(EBCD) = ¾ × 108 = 81
Now, Area(∆EOD) = Area(EBCD) – [Area(∆EOB) + Area(∆BOF) + Area(∆FOC) + Area(∆COD)] = 81 – 72 = 9
Hence, 9.
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