In figure, ABCD is a parallelogram, \(AE\bot DC\)and \(CF\bot AD\). If AB = 16cm, AE = 8 cm and CF = 10 cm, find AD.

3

(a)

A villager Itwaari has a plot of  land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plotfrom one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

3

(a)

ABCD is a' trapezium with AB || DC A line parallel to AC intersects AB at X and BC at Y. Prove that ar(\(\Delta \) ADX) = ar(\(\Delta \) ACY)

3

(a)

In figure, AP || BQ || CR. Prove that ar(\(\Delta \)AQC) = ar(\(\Delta \)PBR).

3

(a)

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(\(\Delta \) AOD) = ar(\(\Delta \) BOC). Prove that ABCD is a trapezium.

3

(a)

MNOP is a parallelogram and PN is one of its diagonals show that ar(\(\Delta\)PMN) = ar(\(\Delta\)PON).

3

(a)

If a parallelogram and a triangle are on the same base and between the same parallels, then prove that area of a triangle is equal to half the area of a parallelogram.

3

(a)

In the figure, ar (\(\Delta\)DRC) = ar(\(\Delta\) DPC) and ar(\(\Delta\)BDP) = ar(\(\Delta\)ARC). Show that both the quarilaterals ABCD and DCPR are trapeziums.

3

(a)

In the figure, AP || BQ || CR. Prove that ar(AQC) = ar(PBR).

3

(a)

In \(\Delta\)GHK; D, E and F are the mid-point of sides HK, KG and GH respectively. show that EFHK is trapezium and ar(EFHK) = \(\frac { 3 }{ 4 } ar(\Delta GHK)\)

3

(a)