ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB.
Prove that (i) ar (ABCD) = ar(ABEF)
(ii) ar (ABCD) = `AB xx DG`

ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD. If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that (i) ar(PQRS) = ar(ABRS) (ii) ar(DeltaAXS) =1/2 ar(PQRS)

In rectangle ABCD, E is the midpoint of side BC. Prove that, AE = DE.

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (DeltaACB) = ar (DeltaACF) (ii) ar (AEDF) = ar (ABCDE)

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that DeltaAFD~=DeltaBEC .

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that (i) DeltaAPB ~= DeltaCQD (ii) AP = CQ

ABCD is a quadrilateral in which AD = BC and /_ DAB = /_ CBA Prove that (i) DeltaABD ~= DeltaBAC (ii) BD = AC (iii) /_ ABD = /_ BAC