Question

in the figure point D is the midpoint of side BC and point G is the centroid of triangle ABC FIND A(AGB)/A(ABD)

Answer 1

Answer:

$\dfrac{ar(AGB)}{ar(ABD)}=\dfrac{2}{3}$

Step-by-step explanation:

Please see the attachment for figure.

D is the mid point of side BC.

Hence, BD=CD

G is centroid of triangle ABC.

As we know centroid divide median in 2:1 ratio.

Hence, AG:GD = 2:1

If two triangles have same base of line and common vertex then their ratio of their area is equal to their base ratio.

$\dfrac{ar(AGB)}{ar(ABD)}=\dfrac{AG}{AD}$

$\dfrac{ar(AGB)}{ar(ABD)}=\dfrac{2}{3}$

Thus, The ratio of ar(AGB):ar(ABD)=2:3