# Quadrilaterals - Page 5

Questions

- Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #64 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
- Given MPRK is a parallelogram, how would you prove, in two-column format, that the measure of angle MTK = measure of angle PMT + measure of angle RKT?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #48 #, how long are the other two sides?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #pi/3 #, what is the area of the parallelogram?
- A parallelogram has sides with lengths of #12 # and #4 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram have lengths of #12 #. If one corner of the parallelogram has an angle of #pi/8 # and the parallelogram's area is #32 #, how long are the other two sides?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #15 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #15 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #160 #, how long are the other two sides?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #9 # and sides C and D have a length of # 4 #. If the angle between sides A and C is #(5 pi)/12 #, what is the area of the parallelogram?
- A parallelogram is determined by the vectors a = (-2,5) and b = (3,2). Determined the angles between the diagonals of the parallelogram?
- Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #24 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #48 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/6 #, what is the difference between the areas of the rhombuses?
- What quadrilateral has no congruent sides?
- Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #26 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #6 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/6 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #48 #, how long are the other two sides?
- A parallelogram has sides with lengths of #7 # and #16 #. If the parallelogram's area is #14 #, what is the length of its longest diagonal?