Triangle and Quadrilateral

1. In the given figure, ABCD is a square and EBCF a parallelogram. If AB = 4cm, calculate the area of the parallelogram EBCF.

Solution:
Length of each side of square ABCD = 4 cm
Area of ABCD = (4)2
= 16 cm2
Area of parm. EBCF = Area of square ABCD
= 16 cm2
[∵ Being parallelograms standing on the same base and between the same parallel lines.]

2. In the given figure, BE = EC, EF⊥ BC, BE = 10 cm and AD = 16 cm, find the area of parallelogram ABCD.



3. A triangle PMN and a parallelogram RMNQ are constructed on the same base MN and between the same parallels MN and PQ. Prove that:

Ar. of ΔPMN =1/2 Ar. of parm. RMNQ



4. Prove that: the area of triangle is half the parallelogram on the same base and between the same parallel lines.


5.  In the figure alongside, if ABCD and ABEF are parallelograms, then prove that: Area of ΔADG = Area of ΔBCH.



6.P is a point on the side AD of a parallelogram ABCD.The straight line through the point C drawn parallel to BP intersects AD produced at Q and the straight line through the point Q drawn parallel to PC intersects BC produced at the point R .prove that :Ar.of parm.CPQR=Ar. Of parm. ABCD.


C
7. In the given figure, AD||BC. If the areas of ΔABE and ΔACF are equal, then prove that: EF||AC


 8.In the adjoining figure, PQRS and LQMN are two parallelograms equal in area. Prove that: LR||SN


9.Two parallelograms KLMN and KLPO lie on the opposite sides of KL in such a way that the points N, K, O are non-collinear. Prove that: (i) NOPM is a parallelogarm. (ii) Ar. of parm. KLMN + Ar. of parm. KLPO = Ar. of parm. NOPM






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