If G is the centroid of a `DeltaABC," Prove that "(" area of "DeltaGAB)" "=(" area of "DeltaGBC)=( "area fo "DeltaGCA)=(1)/(3)(" area of "DeltaABC)`

In the figure ''P'' is a point in the interior of a parallelogram ABCD. Show that area of DeltaAPD+ area of DeltaPBC = area of DeltaAPB+ area of DeltaPCD .

In the figure , DE || BC and (AD)/(DB) = 3/5 , calculate the value of (i) ("area of " Delta ADE)/("area of " Delta ABC) (ii) ("area of trapezium BCED")/("area of " Delta ABC)

Internal bisectors of DeltaABC meet the circumcircle at point D, E, and F Area of DeltaDEF is

In Delta ABC , I is the incentre, Area of DeltaIBC, DeltaIAC and DeltaIAB are, respectively, Delta_(1), Delta_(2) and Delta_(3) . If the values of Delta_(1), Delta_(2) and Delta_(3) are in A.P., then the altitudes of the DeltaABC are in

Given A(1,1,1) , B(1, 2, 3) and C(2, 3, 1) are the vertices of DeltaABC . Find the area of DeltaABC .

Let O be a point inside DeltaABC such that angleOAB = angleOBC = angle OCA = theta Area of DeltaABC is equal to

Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + 3bar(OC) = 0 . Then the ratio of a DeltaABC to area of DeltaAOC is

In triangle ABC, if P, Q, R divides sides BC, AC, and AB, respectively, in the raito k : 1 (in order). If the ratio (("area "DeltaPQR)/("area " DeltaABC)) " is " (1)/(3) , then k is equal to