Area of a triangle is equal to

In the figure, the area of parallelogram PQRS is:

If length of the diagonal of a square is 8 cm, then its area will be

In the following figure, ABCD is a parallelogram. \(DE\bot AB\) and \(BF\bot AD\). If AB = 12 cm, DE = 6 cm and AD = 8 cm, find BF.

If a triangle and a parallelogram are on same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is

In \(\Delta\)ABC, E is the mid-point of median AD, then the ratio of area of \(\Delta\)BED to the area \(\Delta\)ABC is _______________

In a parallelogram ABCD, AB = 8 cm. The altitudes corresponding to sides AB and AD are respectively 4 cm and 5 cm. Find measure of AD.

If the area of parallelogram (shown in figure) is 80 cm² , then find area of \(\Delta \) ADP.

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

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)

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) = \(\frac { 3 }{ 4 } ar(\Delta GHK)\)

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

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

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.

ABCD is a quadrilateral with BD as one of its diagonals and AB = CD=2.5 cm, \(\angle ABD=\angle CDB\) = 90\(°\) and DB = 4 cm. Show that quad. ABCD is a parallelogram and find its area.

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

In \(\Delta\)ABC, medians BE and CD are produced respectively to points X and Y such that CD=DX and BE=EY as shown in figure. Show the points X, A and Y are collinear. Also, show that A is the mid-point of XY.

In the given figure ABCD and AEFD are two parallelograms. Prove that ar(\(\Delta\)PEA)=ar(\(\Delta\)QFD).

A villager had a plot of land in the shape of a quadrilateral. The Gram Panchayat decided to take come portion of his plot from one of the corners to construct a Health Centre. He reluctantly agrees but with a condition that he will be given equal amount of land in lieu of his plot so as to form a triangular plot.
Answer the following questions:
(i) Explain how could this be implemented with figure?
(ii) what value of the villager is depicted hare?
(iiii) Do you thick constructing a Health Centre in the village is justified.If so, why?