Question

if a triangle and parallelogram are on the same base and between tje same parallels then prove that the areaof the triangle is equal to half of the area of the parallelogram​

Answer 1

let ABC and a parallelogram ABCD be on the same base and between same parallel Ab and PC

Draw BQ || AP obtain another parallelogram. ABQP and ABCD are on the same base AB and between the same parallels AB and PC

ar ( ABQP) = ar( ABCD) ------------ (1 )

But ABC congruent to BQP (diagonals PB divide parallelogram ABQP into two congruent

So,,, ar ( PAB) = ar ( BQP) ------- ( 2 )

ar( PAB) = 1 / 2 ar ( ABQP ) ---------- ( from 2 )

This gives ar ( PAB) = 1/2 ar ( ABCD ) ------ { From (1) and (3) }

Hence proved .....