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Areas of Parallelograms and Triangles Worksheets

1.

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

2.

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

3.

Diagonals AC and BD of a trapezium ABCD with ABDC intersect each other at O. Prove that ar (AOD) = ar (BOC).

4.

. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that

ar() = ar()

5.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

6.

In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC).

7.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(APB) = ar(BQC).

8.

If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that

ar (EFGH) = 1/2 ar(ABCD).

9.

In triangle PQR, S and T are points on PQ and PR respectively. If ar (QSR) = ar (QTR). Show that

10.

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle?

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