Yes. If the diagonals bisect the angles, the quadrilateral is always a parallelogram, specifically, a rhombus.
Consider quadrilateral ABCD. If diagonal AC bisects angles A and C, then ΔACB is congruent to ΔACD (ASA). Hence AB=AD and BC=CD (CPCTC).
Likewise, if diagonal BD bisects angles B and D, triangles BDA and BDC are congruent, thus AB=BC and AD=CD. (CPCTC again). Now, we have AB=BC=CD=AD, so the figure is a rhombus, hence a parallelogram.
We have to calculate the volume of the right rectangular prism.
lenght=4 1/2 in=(4+1/2) in=9/2 in
width=5 in
height=3 3/4 in=(3+3/4) in=15/4 in
Volume (right rectangular prism = lenght x width x height.
volume=9/2 in * 5 in * 15/4 in=675/8 in³
we calculate the volume of this little cube.
volume=side³
volume=(1/4 in )³=1/64 in³
Now, we calculate the number of small cubes are needed to fit the right rectangular pris by the rule of three.
1 small cube----------------1/64 in³
x---------------------------------675/8 in³
x=(1 small cube * 675/8 in³) / 1/64 in³=5400 small cubes.
Answer: we need 5400 small cubes to fit the right rectangular prism.
