Q.1. P and R are point on side CD of a parallelogram ABCD . Show that (i). ar (triangle PAB) = ar(triangle RAB) (ii). aIf ar (triangle PAB) = 8 cm square, find ar (ABCD) Q.2. Prove that equal chords of two congruent circles subtend equal angles at their centers . Q.3. Construct a square whose each side measure 5 cm . Q.4. ABCD is a parallelogram in which diagonal BD bisects angle B . Show that BD bisects angle D also . Q.5. A 4 cm wooden cube is cut into 1 cm cubes . What is the percentage increase in the surface area after such cutting ?

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Q1 : 

\triangle PAB and \triangle RAB have same base AB.
Since they lie between parallel sides, the height is also same.
Consequently areas will be same.
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See diagram.

Take AB as the base of the parallelogram.
Then  draw perpendiculars from P and R on to AB.  Since  AB || CD,  the two perpendiculars are parallel and equal to the altitude of the parallelogram with AB as the base.

 The area of triangle PAB = area of RAB = 1/2 * AB * altitude.
  Area of parallelogram ABCD =  AB * altitude  = twice that of the triangles.
                       =  16 cmsquare.
see diagram.
   Take a circle of radius R.  Two congruent circles mean that their radii are same.  So we can work with one circle itself.    So I draw two chords AB and DE  of equal length L.  C is the center of circle.
  Look at the triangles CAB and CDE.  The sides  AB = DE, given.  Then CA = CB = CD = CE = radius of the triangle.  Hence the two triangles are congruent.  Hence angles  ACB and angle DCE are same.  So the angles subtended are same.
     Draw a line horizontally in the middle of paper sheet, and measure 5 cm using a ruler.  Mark the end points as A and B.  Now using the perpendicular bisector method using compass or by using protractor draw a line AD at A and  a line BC at B , both perpendicular to the line AB.  Use the ruler or the compass measuring 5 cm, to cut off these BC and AD at 5 cm.  Now join CD.   
you have the square.
4  In parallelogram ABCD, the diagonal BD bisects angle B.  Means that
         angle ABD = angle DBC.
   AD || BC.  and BD is a transversal line cutting the two parallel lines.
   Hence,  we have  angle ADB = angle DBC  as they are alternate angles.
                             also angle ABD = angle BDC  as they are  alternate angles.
             Since angle ABD = angle DBC, the other two angles ADB = angle BDC.
   So BD bisects  angle D also.

cube edge length = 4 cm
its total  surface are a =  6 * 4²  = 96 cm²

volume of the cube = 4³ = 64 cm³
volume of small cubes  =  1³ cm³
number of small cubes made from the big cube :  64 cm³/1 cm³ = 64
surface area of all 64 small cubes : 64 * 6 * 1² = 384 cm²

increase in surface area =  384 - 96 = 288 cm²
% increase =  288/96 * 100 =  300%

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