ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

 

4

(a)

In the given figure, AB 11DC. Show that ar(BDE) = ar(ACED).
     
 

4

(a)

Areas of triangles on the same bases and between the same parallels are equal in. Prove it.

4

(a)

In the given figure, ABED is a parallelogram in which DE = EC. Show that: area (ABF) = area (BEC).

4

(a)

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.

4

(a)

Given two points A and B and a positive real number k. Find the locus of a point P such that ar(\(\Delta \) PAB) = k.

4

(a)

BD is one of the diagonals of a quadrilateral AB CD. AM and CN are the perpendiculars from A and C respectively on BD. Show that
\(ar(ABCD)=\frac { 1 }{ 2 } BD.(AM+CN)\).

4

(a)

PQRS is a parallelogram and O is a point in the interior of the parallelogram. Show that ar(POS) + ar(QOR)=\(\frac { 1 }{ 2 } ar(PQRS)\).

4

(a)

In \(\Delta\)ABC, E is the mid-point of median AD. show that ar(\(\Delta\)BED) = \(\frac { 1 }{ 4 } ar(\Delta ABC)\)

4

(a)

Two brothers have a triangular plot. They decide to distribute it equally amongst themselves but also want to give away a triangular part of it for charity to a school which is attached on the base side of 120 m of the triaangular plot.
Answer the following questions:
(i) what is the area of the triangular plot if its height is 90 m?
(ii) Explain with the help of figure how could this be possible and what type of parts do the brothers get?
(iii) What value of the two brothers is depicted here?

4

(a)