# Quadrilaterals - Page 4

Questions

- Two opposite sides of a parallelogram have lengths of #7 #. If one corner of the parallelogram has an angle of #pi/12 # and the parallelogram's area is #16 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #32 #, how long are the other two sides?
- A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- Can a rhombus be a kite?
- A quadrilateral has two pair of opposite parallel sides. Each of one pair of parallel sides is 4 yards long. Each of the second pair of sides is 8 yards long. A diagonal connecting the opposite corners of the quadrilateral is 9 yards long. Is rectangle?
- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #(pi)/2 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- 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 # 4 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/8 # and the parallelogram's area is #36 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #11 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?
- Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(pi)/6 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #72 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?
- Is a rectangle a parallelogram always, sometimes or never?
- 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 #36 #, how long are the other two sides?
- It is given that line MO = line TR and line NP = line QS, where MNOP and TQRS are parallelograms. A student has said that if those statements are true, then MNOP = TQRS. Why is this student incorrect?
- Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?